We want to factor the following expression: (x+7)^(2)+2y(x+7)+y^(2) Which pattern can we use to factor the expression? U and V are either constant integers or single-variable expressions. Choose 1 answer: (A) (U+V)^(2) or (U-V)^(2) (B) (U+V)(U-V) (c) We can't use any of the patterns.

Recognize the structure: Recognize the structure of the given expression. The given expression is (x+7)^(2)+2y(x+7)+y^(2). We can observe that it has three terms: a square of (x+7), a product of 2y and (x+7), and a square of y.Identify the pattern: Identify the pattern that matches the structure of the expression. The expression resembles the square of a binomial pattern, which is (U+V)^(2) or (U-V)^(2), where the first term is U^2, the second term is 2UV, and the third term is V^2.Match with square of binomial: Match the terms of the expression with the square of a binomial pattern. In our case, U is (x+7) and V is y. The expression fits the pattern (U+V)^(2) because: - The first term (x+7)^(2) is U^2. - The second term 2y(x+7) is 2UV. - The third term y^(2) is V^2.Write the factored form: Write the factored form using the identified pattern. Since the expression fits the pattern (U+V)^(2), we can write the factored form as ((x+7)+y)^(2).

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We want to factor the following expression:

(x+7)^(2)+2y(x+7)+y^(2)
Which pattern can we use to factor the expression?

U and
V are either constant integers or single-variable expressions.
Choose 1 answer:
(A)
(U+V)^(2) or
(U-V)^(2)
(B)
(U+V)(U-V)
(c) We can't use any of the patterns.

We want to factor the following expression: $\newline$ $(x+7)^{2}+2 y(x+7)+y^{2}$ $\newline$ Which pattern can we use to factor the expression? $\newline$ $U$ and $V$ are either constant integers or single-variable expressions. $\newline$ Choose $1$ answer: $\newline$ (A) $(U+V)^{2}$ or $(U-V)^{2}$ $\newline$ (B) $(U+V)(U-V)$ $\newline$ (C) We can't use any of the patterns.

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Algebra 1

Compare linear and exponential growth

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Q. We want to factor the following expression:

\newline

(x+7)^{2}+2 y(x+7)+y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

and

V

are either constant integers or single-variable expressions.

\newline

Choose

1

answer:

\newline

(A)

(U+V)^{2}

(U-V)^{2}

\newline

(B)

(U+V)(U-V)

\newline

Recognize the structure: Recognize the structure of the given expression. $\newline$ The given expression is x+7)^{2}+2y(x+7)+y^{2}\. We can observe that it has three terms: a square of \$x+7, a product of $2y$ and $x+7$ , and a square of $y$ .
Identify the pattern: Identify the pattern that matches the structure of the expression. $\newline$ The expression resembles the square of a binomial pattern, which is $(U+V)^{2}$ or $(U-V)^{2}$ , where the first term is $U^2$ , the second term is $2UV$ , and the third term is $V^2$ .
Match with square of binomial: Match the terms of the expression with the square of a binomial pattern. $\newline$ In our case, $U$ is $(x+7)$ and $V$ is $y$ . The expression fits the pattern $(U+V)^{2}$ because: $\newline$ - The first term $(x+7)^{2}$ is $U^2$ . $\newline$ - The second term $2y(x+7)$ is $2UV$ . $\newline$ - The third term $y^{2}$ is $(x+7)$ $0$ .
Write the factored form: Write the factored form using the identified pattern. $\newline$ Since the expression fits the pattern $(U+V)^{2}$ , we can write the factored form as $((x+7)+y)^{2}$ .