Question

Multiply the expressions. $$(5 a-4 b)(2 a-b)$$

   Multiply the expressions.
$$(5 a-4 b)(2 a-b)$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 5, Problem 94

Instant Answer

Solved by Expert Julie Silva

03/24/2021

Step 1

The FOIL method stands for First, Outside, Inside, Last. This means we multiply the first terms in each binomial, then the outside terms, then the inside terms, and finally the last terms. So, we start by multiplying the first terms in each binomial, which are Show more…

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Multiply the expressions. $$(5 a-4 b)(2 a-b)$$

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Key Concepts

Distributive Property

This property states that multiplying a sum by a number is the same as doing each multiplication separately. In the context of multiplying polynomials, each term in the first expression must be multiplied by each term in the second expression.

FOIL Method

The FOIL method is a specialized approach for multiplying two binomials. It stands for First, Outer, Inner, Last, referring to the order in which pairs of terms are multiplied to ensure that all products are accounted for when expanding the expression.

Combining Like Terms

After performing the multiplication, similar terms in the resulting polynomial are combined by adding their coefficients. This step is essential for simplifying the expression to its most reduced form.

Polynomial Multiplication

This concept encompasses the process of multiplying polynomials, where methods like the distributive property and the FOIL method are used. It is fundamental in algebra for expanding expressions and simplifying equations involving multiple terms.

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