Algebraic Expressions
2026-02-28 01:45 Diff
https://brightchamps.com/en-us/math/algebra/algebraic-expressions

We solve algebraic expressions using arithmetic operations. These mathematical operations help us in differentiating and simplifying the terms in an expression.

We will now discuss the four operations of algebraic expression:


Addition of Algebraic Expressions


We use addition to add up the terms that have the same exponents and variables (like terms). 

For example: \((2x + 3y + 6) + (5x + 9 + y + 8).\)

To find the sum, we will combine the like terms:

\((2x + 5x) + (3y + 9y) + (6 + 8)\)

\(7x + 12y + 14\)


Subtraction of Algebraic Expressions


In the subtraction method, we will first remove the negative sign and then combine the similar terms.

For example: \((3a + 4b – 2) – (5a – 6b + 8)\)

Let’s first give out the negative sign:

\(3a + 4b – 2 – 5a + 6b – 8\)

To subtract the expression, we combine the like terms: 

\((3a – 5a) + (4b + 6b) + (– 2 – 8)\)

\(–2a + 10b – 10\)

Multiplication of Algebraic Expressions


Terms can be expanded and multiplied by applying the distributive property 

\((9x + 4) (2x – 6)\)

Let’s multiply the terms using distributive property:

\((9x) (2x) + (9x) (– 6) + 4 (2x) + 4 (– 6)\)

\(18x^2 – 54x + 8x – 24\)

\(18x^2 – 46x – 24\).

Division of Algebraic Expressions


The division of algebraic expressions involves taking out and eliminating common terms. The division of algebraic expressions is in two ways : monomial and polynomial division.

  • Monomial division: 

    \(\frac{16 y^3} {4y}\) \(= \frac{16}{4} = 4\)
    (Dividing coefficients)
    Now we subtract the exponents: \(y^3 ÷ y^1 = y^{3-1} = y^2\) \(= 4y^2\)

  • Polynomial Division:   

    \((12x^2 + 6x) ÷  2x\)

    Now we will divide each term individually:

    \(\frac{12x^2}{2x} + \frac{6x}{2x}\)

     \(=6x + 3\)