We want to factor the following expression: (x+5)^(4)+2(x+5)^(2)-1 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+5)^(4)+2(x+5)^(2)-1. We can see that it resembles a quadratic in form, where (x+5)^(2) can be considered as a single variable, let's call it U. So the expression can be rewritten as U^2 + 2U - 1, where U = (x+5)^(2).Identify the factoring pattern: Identify the factoring pattern. The rewritten expression U^2 + 2U - 1 is a quadratic expression and does not fit the perfect square patterns (U+V)^(2) or (U-V)^(2), nor does it fit the difference of squares pattern (U+V)(U-V). However, it can be factored using the methods for factoring a quadratic expression, which is not listed in the given choices.Determine if given patterns apply: Determine if any of the given patterns apply. Since the expression is a quadratic in U and does not fit the given patterns (A) or (B), and since we can factor it using methods for factoring quadratics, the correct answer is (C) We can't use any of the patterns.

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We want to factor the following expression:

(x+5)^(4)+2(x+5)^(2)-1
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: $\newline$ $(x+5)^{4}+2(x+5)^{2}-1$ $\newline$ 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+5)^{4}+2(x+5)^{2}-1

\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 $(x+5)^{4}+2(x+5)^{2}-1$ . We can see that it resembles a quadratic in form, where $(x+5)^{2}$ can be considered as a single variable, let's call it $U$ . So the expression can be rewritten as $U^{2} + 2U - 1$ , where $U = (x+5)^{2}$ .
Identify the factoring pattern: Identify the factoring pattern. $\newline$ The rewritten expression $U^2 + 2U - 1$ is a quadratic expression and does not fit the perfect square patterns $(U+V)^{2}$ or $(U-V)^{2}$ , nor does it fit the difference of squares pattern $(U+V)(U-V)$ . However, it can be factored using the methods for factoring a quadratic expression, which is not listed in the given choices.
Determine if given patterns apply: Determine if any of the given patterns apply. $\newline$ Since the expression is a quadratic in $U$ and does not fit the given patterns $(A)$ or $(B)$ , and since we can factor it using methods for factoring quadratics, the correct answer is $(C)$ We can't use any of the patterns.