Question

Multiply the binomials. $(4 a+b)(3 a-5 b)$

   Multiply the binomials.
$(4 a+b)(3 a-5 b)$

Intermediate Algebra

Intermediate Algebra

Lisa Healey 1st Edition

Chapter 4, Problem 25

Instant Answer

Solved by Expert Ankit Gupta

06/18/2020

Step 1

Step 1: Identify the binomials to be multiplied: \((4a + b)\) and \((3a - 5b)\). Show more…

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Multiply the binomials. $(4 a+b)(3 a-5 b)$

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Key Concepts

Distributive Property

The distributive property is a fundamental algebraic property that allows you to multiply a single term by each term inside a parenthesis. When multiplying binomials, this property is applied to ensure every term in the first binomial is multiplied by every term in the second binomial, producing all the necessary terms for further simplification.

FOIL Method

The FOIL method is a specific application of the distributive property that is used for multiplying two binomials. It stands for First, Outer, Inner, Last, indicating the order in which to multiply the terms of the binomials. This method provides a systematic approach to ensure that all combinations of terms are multiplied correctly.

Combining Like Terms

After applying the distributive property or the FOIL method, the resulting expression typically includes several terms that may be similar. Combining like terms involves adding or subtracting coefficients of terms that have the same variables raised to the same powers, which simplifies the overall expression.

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