How To Do Multiplication of Algebraic Expressions?

To perform multiplication of algebraic expressions:

• Identify like terms.
• Apply the distributive property when multiplying binomials or a monomial by a polynomial.
• Combine like terms after multiplication.

Multiplication of Two Monomials

When multiplying two monomials, multiply the coefficients together and combine the variables by adding their exponents.

Example: Multiply 3x² and 4x³.

Solution:

(3x²)(4x³) = 12x^{2+3} = 12x⁵

Multiplication of a Polynomial by a Monomial

To multiply a polynomial by a monomial, distribute the monomial across each term of the polynomial.

Example: Multiply 2x and 3x² + 4x + 1.

Solution:

2x(3x² + 4x + 1) = 6x³ + 8x² + 2x

Multiplication of Two Binomials

When multiplying two binomials, apply the distributive property by multiplying each term of one binomial by each term of the other binomial and then combine like terms.

Example: Multiply x – 2 and 3x – 1.

Solution:

(x + 2)(3x – 1) = 3x² + 5x – 2

Multiplication of Two Polynomials

Multiplying by a polynomial involves distributing each term of the polynomial across the terms of the other expression then combining like terms. This is explained by the example added below as,

Example: Multiply 2x² + x – 11 and 3x² + 4x – 1.

Solution:

(2x² + x – 11)(3x² + 4x – 1)

= 2x²(3x² + 4x – 1) + x(3x² + 4x – 1) – 11(3x² + 4x – 11)

= 6x⁴ + 8x³ – 2x² + 3x³ + 4x² -x – (33x² + 44x – 121)

= 6x⁴ + 8x³ + 3x³ – 2x² + 4x² – 33x² – 44x + 121

= 6x⁴ + 11x³ – 31x² – 44x + 121

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.