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

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 48

1장, 문제 48

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

검증된 단계별 안내

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}

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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