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2026-01-01
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2026-02-28
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<p>128 Learners</p>
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<p>160 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>In mathematics, the expansion of an algebraic expression such as (a + b + c)² is essential for understanding polynomial expressions and simplification techniques. In this topic, we will learn the formula for expanding (a + b + c)².</p>
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<p>In mathematics, the expansion of an algebraic expression such as (a + b + c)² is essential for understanding polynomial expressions and simplification techniques. In this topic, we will learn the formula for expanding (a + b + c)².</p>
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<h2>Math Formula for (a + b + c)²</h2>
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<h2>Math Formula for (a + b + c)²</h2>
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<h2>Formula for (a + b + c)²</h2>
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<h2>Formula for (a + b + c)²</h2>
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<p>The formula to expand (a + b + c)² is:</p>
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<p>The formula to expand (a + b + c)² is:</p>
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<p>(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.</p>
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<p>(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.</p>
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<h2>Importance of the (a + b + c)² Formula</h2>
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<h2>Importance of the (a + b + c)² Formula</h2>
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<h3>Explore Our Programs</h3>
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<h3>Explore Our Programs</h3>
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<h2>Tips and Tricks to Memorize the (a + b + c)² Formula</h2>
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<h2>Tips and Tricks to Memorize the (a + b + c)² Formula</h2>
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<p>Students find algebraic formulas challenging.</p>
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<p>Students find algebraic formulas challenging.</p>
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<p>Here are some tips to master the (a + b + c)² formula:</p>
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<p>Here are some tips to master the (a + b + c)² formula:</p>
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<ul><li>Remember it as the<a>sum</a>of<a>squares</a>of each term: a², b², c². </li>
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<ul><li>Remember it as the<a>sum</a>of<a>squares</a>of each term: a², b², c². </li>
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<li>Add the cross terms: 2ab, 2bc, 2ca. </li>
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<li>Add the cross terms: 2ab, 2bc, 2ca. </li>
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<li>Visualize it geometrically as the area of a square with sides (a + b + c).</li>
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<li>Visualize it geometrically as the area of a square with sides (a + b + c).</li>
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</ul><h2>Real-Life Applications of the (a + b + c)² Formula</h2>
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</ul><h2>Real-Life Applications of the (a + b + c)² Formula</h2>
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<p>The (a + b + c)² formula is used in various real-life applications, including: </p>
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<p>The (a + b + c)² formula is used in various real-life applications, including: </p>
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<ul><li>Calculating the area of shapes with three combined linear dimensions. </li>
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<ul><li>Calculating the area of shapes with three combined linear dimensions. </li>
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<li>Simplifying complex<a>expressions</a>in physics and engineering, such as computing forces or energy levels.</li>
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<li>Simplifying complex<a>expressions</a>in physics and engineering, such as computing forces or energy levels.</li>
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</ul><h2>Common Mistakes and How to Avoid Them While Using the (a + b + c)² Formula</h2>
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</ul><h2>Common Mistakes and How to Avoid Them While Using the (a + b + c)² Formula</h2>
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<p>Students often make errors when expanding (a + b + c)². Here are some mistakes and how to avoid them.</p>
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<p>Students often make errors when expanding (a + b + c)². Here are some mistakes and how to avoid them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Expand (x + y + z)².</p>
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<p>Expand (x + y + z)².</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The expansion is x² + y² + z² + 2xy + 2yz + 2zx.</p>
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<p>The expansion is x² + y² + z² + 2xy + 2yz + 2zx.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the formula (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, substitute a = x, b = y, c = z to get x² + y² + z² + 2xy + 2yz + 2zx.</p>
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<p>Using the formula (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, substitute a = x, b = y, c = z to get x² + y² + z² + 2xy + 2yz + 2zx.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>What is the expansion of (2m + 3n + 4p)²?</p>
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<p>What is the expansion of (2m + 3n + 4p)²?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The expansion is 4m² + 9n² + 16p² + 12mn + 24np + 16mp.</p>
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<p>The expansion is 4m² + 9n² + 16p² + 12mn + 24np + 16mp.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Substitute a = 2m, b = 3n, c = 4p into the formula (a + b + c)² to get 4m² + 9n² + 16p² + 12mn + 24np + 16mp.</p>
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<p>Substitute a = 2m, b = 3n, c = 4p into the formula (a + b + c)² to get 4m² + 9n² + 16p² + 12mn + 24np + 16mp.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Find the expansion of (a + 2b + 3c)².</p>
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<p>Find the expansion of (a + 2b + 3c)².</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The expansion is a² + 4b² + 9c² + 4ab + 12bc + 6ac.</p>
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<p>The expansion is a² + 4b² + 9c² + 4ab + 12bc + 6ac.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the formula (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, substitute a = a, b = 2b, c = 3c to get a² + 4b² + 9c² + 4ab + 12bc + 6ac.</p>
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<p>Using the formula (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, substitute a = a, b = 2b, c = 3c to get a² + 4b² + 9c² + 4ab + 12bc + 6ac.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the (a + b + c)² Formula</h2>
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<h2>FAQs on the (a + b + c)² Formula</h2>
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<h3>1.What is the formula for (a + b + c)²?</h3>
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<h3>1.What is the formula for (a + b + c)²?</h3>
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<p>The formula to expand (a + b + c)² is: a² + b² + c² + 2ab + 2bc + 2ca.</p>
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<p>The formula to expand (a + b + c)² is: a² + b² + c² + 2ab + 2bc + 2ca.</p>
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<h3>2.Why is the (a + b + c)² formula important?</h3>
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<h3>2.Why is the (a + b + c)² formula important?</h3>
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<p>It is important because it helps simplify expressions and solve problems involving polynomials and quadratic equations.</p>
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<p>It is important because it helps simplify expressions and solve problems involving polynomials and quadratic equations.</p>
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<h3>3.How do you derive the (a + b + c)² formula?</h3>
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<h3>3.How do you derive the (a + b + c)² formula?</h3>
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<p>Derive it by using the distributive property: (a + b + c)² = (a + b + c)(a + b + c) and expand by multiplying each term.</p>
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<p>Derive it by using the distributive property: (a + b + c)² = (a + b + c)(a + b + c) and expand by multiplying each term.</p>
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<h3>4.Can (a + b + c)² be used in geometry?</h3>
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<h3>4.Can (a + b + c)² be used in geometry?</h3>
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<p>Yes, it can be used to find the area of squares or rectangles formed by combining three linear dimensions.</p>
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<p>Yes, it can be used to find the area of squares or rectangles formed by combining three linear dimensions.</p>
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<h2>Glossary for the (a + b + c)² Formula</h2>
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<h2>Glossary for the (a + b + c)² Formula</h2>
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<ul><li><strong>Square:</strong>The result of multiplying a<a>number</a>or expression by itself.</li>
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<ul><li><strong>Square:</strong>The result of multiplying a<a>number</a>or expression by itself.</li>
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</ul><ul><li><strong>Expansion:</strong>Expressing a mathematical expression as a sum<a>of terms</a>.</li>
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</ul><ul><li><strong>Expansion:</strong>Expressing a mathematical expression as a sum<a>of terms</a>.</li>
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</ul><ul><li><strong>Polynomial:</strong>An algebraic expression of<a>variables</a>and coefficients.</li>
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</ul><ul><li><strong>Polynomial:</strong>An algebraic expression of<a>variables</a>and coefficients.</li>
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</ul><ul><li><strong>Distributive Property:</strong>A property that distributes<a>multiplication</a>over<a>addition</a>.</li>
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</ul><ul><li><strong>Distributive Property:</strong>A property that distributes<a>multiplication</a>over<a>addition</a>.</li>
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</ul><ul><li><strong>Cross Terms:</strong>Terms in an expansion that involve the<a>product</a>of two different variables.</li>
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</ul><ul><li><strong>Cross Terms:</strong>Terms in an expansion that involve the<a>product</a>of two different variables.</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>