Question

Find each product. $$ (2 x+3)(6 x-4) $$

   Find each product.
$$
(2 x+3)(6 x-4)
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 4, Problem 55

Instant Answer

Solved by Expert James Kiss

02/08/2022

Step 1

The FOIL method stands for First, Outer, Inner, and Last. This means we multiply the first terms in each binomial, then the outer terms, then the inner terms, and finally the last terms. Show more…

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Find each product. $$ (2 x+3)(6 x-4) $$

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Key Concepts

Distributive Property

The distributive property is a fundamental algebraic principle that allows you to multiply a single term by each term inside a parenthesis. It is used to expand expressions where a term outside the parentheses distributes over the sum or difference of multiple terms. This concept is key in polynomial multiplication and is applicable in many areas of algebra.

FOIL Method

The FOIL method is a mnemonic used specifically for multiplying two binomials. The acronym stands for First, Outer, Inner, Last, referring to the pairs of terms that are multiplied together. This method provides a systematic approach to ensure all parts of the binomials are multiplied, resulting in a proper expansion of the product.

Combining Like Terms

After distributing the terms in polynomial multiplication, the next crucial step is combining like terms—terms that have the same variables raised to the same powers. This process simplifies the expression and consolidates it into a standard form for easier interpretation and further manipulation in algebra.

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