Find each product. See Examples 5 and 6.(a−6b)2 $$(a-6b)^2$$

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 48

Chapter 1, Problem 48

Find each product. See Examples 5 and 6.
$open paren a minus 6 b close paren squared$

Verified step by step guidance

Recognize that the expression

(a - 6 b))^{2}

is a binomial squared, which can be expanded using the formula for the square of a difference:

(x - y))^{2} = x^{2} - 2 x y + y^{2}

Identify the terms

x

and

y

in the expression: here,

x = a

and

y = 6 b

Calculate the square of the first term:

a^{2}

Calculate twice the product of the two terms:

2 \cdot a \cdot 6 b = 2 \cdot a \cdot 6 \cdot b

Calculate the square of the second term:

6^{2} \cdot b^{2}

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Binomial Squares

A binomial square is the product of a binomial multiplied by itself, expressed as (a + b)² or (a - b)². It expands to a² ± 2ab + b², where the middle term's sign depends on the binomial's sign. Recognizing this pattern simplifies squaring expressions like (a - 6b)².

Distributive Property

The distributive property allows multiplication over addition or subtraction, such as a(b + c) = ab + ac. It is essential for expanding products of binomials by multiplying each term in the first binomial by each term in the second.

Combining Like Terms

After expanding expressions, like terms (terms with the same variables and exponents) must be combined to simplify the expression. This step ensures the final answer is in its simplest form, such as combining terms involving 'ab' in the expansion.

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Combinations

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Multiply or divide, as indicated. ac + ad + bc + bd/a² - b² * a³ - b³/2a² + 2ab + 2b²

Find each product. See Examples 5 and 6.(a−6b)2 (a-6b)^2

Verified video answer for a similar problem:

Key Concepts

Binomial Squares

Distributive Property

Combining Like Terms

Find each product. See Examples 5 and 6.
$open paren a minus 6 b close paren squared$