Question

Use FOIL to multiply. $$ (4 a-5 b)(3 a+4 b) $$

   Use FOIL to multiply.
$$
(4 a-5 b)(3 a+4 b)
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 6, Problem 47

Instant Answer

Solved by Expert Kristen Marte

02/24/2021

Step 1

FOIL stands for First, Outer, Inner, Last. This means we multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms. So, we have: First: $4a \times 3a = 12a^2$ Outer: $4a \times 4b = 16ab$ Inner: $-5b Show more…

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Use FOIL to multiply. $$ (4 a-5 b)(3 a+4 b) $$

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Key Concepts

Combining Like Terms

After applying the distributive property or the FOIL method, the resulting expression often contains similar terms. Combining like terms simplifies the expanded expression by adding or subtracting coefficients of matching variables, leading to a more concise and manageable polynomial.

FOIL Method

The FOIL method is a mnemonic that stands for First, Outside, Inside, Last, and it provides a systematic approach to multiplying two binomials. By multiplying the first terms, the outer terms, the inner terms, and the last terms, one can efficiently expand the product into a polynomial form.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. This property underlies the FOIL method and is essential when multiplying any polynomial expressions, ensuring that each term of one polynomial is properly multiplied with every term of the other.

Binomials

Binomials are algebraic expressions that consist of two terms, typically separated by a plus or minus sign. Understanding binomials is crucial for applying methods like FOIL, as these expressions are a common form encountered in algebraic multiplication and factoring problems.

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