Solved Examples on Multiplication of Algebraic Expression

Example 1: Multiply the given algebraic expression (3x + 2)(4x – 5).

Solution:

Using FOIL Method:

(3x + 2)(4x − 5)

⇒ 3x⋅4x + 3x⋅(−5) + 2⋅4x + 2⋅(−5)

⇒ 12x² − 15x + 8x − 10

⇒ 12x² − 7x − 10

Simplified algebraic expression = 12x² − 7x − 10

Example 2: Find the product of given algebraic expression (a – 2)(a + 3).

Solution:

Using FOIL Method: 

(a − 2)(a + 3)

⇒ a⋅a + a⋅3 − 2⋅a − 2⋅3

⇒ a² + 3a − 2a − 6

⇒ a² + a − 6

Simplified algebraic expression = a² + a − 6

Example 3: Multiply given algebraic expression: (2x² – 3)(x + 4).

Solution:

Using FOIL Method:  

(2x² − 3)( x + 4)

⇒ 2x²⋅x + 2x²⋅4 − 3⋅x − 3⋅4

⇒ 2x³ + 8x² − 3x − 12

Simplified algebraic expression = 2x³ + 8x² − 3x − 12

Example 4: Multiply: (5a – 2b)(3a + b).

Solution:

Using FOIL Method:

(5a − 2b)(3a + b)

⇒ 5a⋅3a + 5a⋅b−2b⋅3a−2b⋅b

⇒ 15a² + 5ab − 6ab −2b²

⇒ 15a² − ab − 2b²

Simplified algebraic expression = 15a² − ab − 2b²

Example 5: Find the product of (2x + 1)(2x – 1).

Solution:

Using FOIL Method:

(2x + 1)(2x − 1)

⇒ 2x⋅2x + 2x⋅(−1) + 1⋅2x −1⋅1

⇒ 4x² − 2x + 2x − 1

⇒ 4x² − 1

Simplified algebraic expression = 4x² − 1

Multiplication of algebraic expressions involves combining algebraic terms using the multiplication operation. The process can involve monomials, binomials, or more complex polynomials.

Algebraic expressions are polynomial equations used in algebra that are used for variety of purposes. Multiplication of algebraic expression is useful for various purposes and it is achieved by multiplying each term of algebraic equation with other algebraic expression.

In this article, we have discuss the concept of multiplication of algebraic expressions, exploring its importance, rules, methods, and practical applications.