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2026-01-01
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2026-02-28
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<p>Operations on expressions involve applying mathematical procedures such as<a>addition</a>,<a>subtraction</a>,<a>multiplication</a>,<a>division</a>, and factoring to expressions involving one or more variables. The main types of operations are: </p>
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<p>Operations on expressions involve applying mathematical procedures such as<a>addition</a>,<a>subtraction</a>,<a>multiplication</a>,<a>division</a>, and factoring to expressions involving one or more variables. The main types of operations are: </p>
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<ul><li>Adding and subtracting expressions </li>
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<ul><li>Adding and subtracting expressions </li>
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<li>Multiplication of expressions </li>
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<li>Multiplication of expressions </li>
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<li>Division of expressions </li>
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<li>Division of expressions </li>
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<li>Solving expressions </li>
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<li>Solving expressions </li>
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<li>Factoring expressions </li>
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<li>Factoring expressions </li>
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<li>Expanding expressions</li>
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<li>Expanding expressions</li>
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</ul><p><strong>Adding and subtracting expressions:</strong>Addition and subtraction are the basic<a>arithmetic operations</a>. In addition, we combine the like terms in the expressions. </p>
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</ul><p><strong>Adding and subtracting expressions:</strong>Addition and subtraction are the basic<a>arithmetic operations</a>. In addition, we combine the like terms in the expressions. </p>
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<p>For example, \((3x + 5) + (5x + 4) = (3x + 5x) + (5 + 4) = 8x + 9\)</p>
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<p>For example, \((3x + 5) + (5x + 4) = (3x + 5x) + (5 + 4) = 8x + 9\)</p>
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<p>In subtracting expressions, the like terms from the second expression are subtracted from the corresponding like terms from the first expression. </p>
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<p>In subtracting expressions, the like terms from the second expression are subtracted from the corresponding like terms from the first expression. </p>
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<p>For example, \((6x+ 3) - (2x + 1) = (6x - 2x) + (3 - 1) = 4x + 2\)</p>
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<p>For example, \((6x+ 3) - (2x + 1) = (6x - 2x) + (3 - 1) = 4x + 2\)</p>
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<p><strong>Multiplication of expressions:</strong>To multiply expressions, we use the<a>distributive property of multiplication</a>, that is, \(a(b + c) = ab + ac\). </p>
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<p><strong>Multiplication of expressions:</strong>To multiply expressions, we use the<a>distributive property of multiplication</a>, that is, \(a(b + c) = ab + ac\). </p>
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<p>For example, multiplying \(3x + 4\) with 5x</p>
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<p>For example, multiplying \(3x + 4\) with 5x</p>
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<p>Using the distributive property of multiplication: \(a(b + c) = ab + ac\)</p>
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<p>Using the distributive property of multiplication: \(a(b + c) = ab + ac\)</p>
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<p>\(5x(3x + 4) = (5x × 3x) + (5x × 4)\\[1em] 5x(3x + 4)= 15x^2 + 20x\)</p>
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<p>\(5x(3x + 4) = (5x × 3x) + (5x × 4)\\[1em] 5x(3x + 4)= 15x^2 + 20x\)</p>
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<p><strong>Division of expressions:</strong>The division of expressions is used to simplify the expressions. Here, the expressions are divided by separate terms, by factoring or simplifying common terms. </p>
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<p><strong>Division of expressions:</strong>The division of expressions is used to simplify the expressions. Here, the expressions are divided by separate terms, by factoring or simplifying common terms. </p>
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<p>For example, \(24x^2 + 36x\) by \(6x\)</p>
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<p>For example, \(24x^2 + 36x\) by \(6x\)</p>
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<p>\((\frac{24x^2}{6x}) + (\frac{36x}{6x}) = 4x + 6\)</p>
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<p>\((\frac{24x^2}{6x}) + (\frac{36x}{6x}) = 4x + 6\)</p>
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<p><strong>Solving expressions:</strong>Solving expressions involves substituting the variables with the given value to find the result. For example, solve \(5x^2 + 5x\) for \(x = 2\) and \(x = 5\)</p>
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<p><strong>Solving expressions:</strong>Solving expressions involves substituting the variables with the given value to find the result. For example, solve \(5x^2 + 5x\) for \(x = 2\) and \(x = 5\)</p>
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<p>If \(x = 2\):</p>
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<p>If \(x = 2\):</p>
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<p>\(5x^2 + 5x = 5(2)^2 + 5(2) = 5(4) + 10 = 20 + 10 = 30\)</p>
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<p>\(5x^2 + 5x = 5(2)^2 + 5(2) = 5(4) + 10 = 20 + 10 = 30\)</p>
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<p>If \(x = 5\): </p>
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<p>If \(x = 5\): </p>
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<p>\(5x^2 + 5x = 5(5)^2 + 5(5) = 5(25) + 25 = 125 + 25 = 150\)</p>
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<p>\(5x^2 + 5x = 5(5)^2 + 5(5) = 5(25) + 25 = 125 + 25 = 150\)</p>
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<p><strong>Factoring expressions:</strong>Factoring expressions is the way of expressing an expression as the<a>product</a>of its factors. In this method, we first factor out the greatest common factor of the expression. </p>
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<p><strong>Factoring expressions:</strong>Factoring expressions is the way of expressing an expression as the<a>product</a>of its factors. In this method, we first factor out the greatest common factor of the expression. </p>
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<p>For example, factoring \(36x + 54\)</p>
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<p>For example, factoring \(36x + 54\)</p>
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<p>The GCF of 36 and 54 is 18</p>
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<p>The GCF of 36 and 54 is 18</p>
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<p>So, \(36x + 54 = 18(2x + 3)\)</p>
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<p>So, \(36x + 54 = 18(2x + 3)\)</p>
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<p><strong>Expanding expressions:</strong>Expanding expressions is the opposite of factoring, as here we remove the parentheses by multiplying the value out of the expression with the expression inside the parentheses. </p>
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<p><strong>Expanding expressions:</strong>Expanding expressions is the opposite of factoring, as here we remove the parentheses by multiplying the value out of the expression with the expression inside the parentheses. </p>
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<p>For example, expanding the expression 18(2x + 3)</p>
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<p>For example, expanding the expression 18(2x + 3)</p>
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<p>\(18(2x + 3) = (18 × 2x) + (18 × 3)\\[1em] 18(2x + 3)= 36x + 54\)</p>
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<p>\(18(2x + 3) = (18 × 2x) + (18 × 3)\\[1em] 18(2x + 3)= 36x + 54\)</p>
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