We want to factor the following expression: (x-2)^(4)-(y+3)^(4) 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.

Identify structure of expression: Identify the structure of the given expression. The given expression is (x-2)^(4)-(y+3)^(4). This resembles the structure of a difference of squares, where one term is squared and subtracted from another term that is also squared.Recall difference of squares pattern: Recall the difference of squares pattern. The difference of squares pattern is a^2 - b^2 = (a + b)(a - b), where a and b can be any expressions.Apply difference of squares pattern: Apply the difference of squares pattern to the given expression. Let U = (x-2)^2 and V = (y+3)^2. Then the given expression can be written as U^2 - V^2, which fits the pattern of a difference of squares.Factor expression using difference of squares: Factor the expression using the difference of squares pattern. Using the pattern from Step 2, we can factor the expression as follows: U^2 - V^2 = (U + V)(U - V) Substitute back U and V: ((x-2)^2 + (y+3)^2)((x-2)^2 - (y+3)^2)Verify factored expression: Verify that the factored expression is equivalent to the original expression. By expanding the factored expression, we should be able to get back to the original expression if our factoring is correct. However, this step is not necessary for choosing the correct pattern, so we can proceed to the answer.

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We want to factor the following expression:

(x-2)^(4)-(y+3)^(4)
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: $\newline$ $(x-2)^{4}-(y+3)^{4}$ $\newline$ 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-2)^{4}-(y+3)^{4}

\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

Identify structure of expression: Identify the structure of the given expression. $\newline$ The given expression is $(x-2)^{4}-(y+3)^{4}$ . This resembles the structure of a difference of squares, where one term is squared and subtracted from another term that is also squared.
Recall difference of squares pattern: Recall the difference of squares pattern. $\newline$ The difference of squares pattern is $a^2 - b^2 = (a + b)(a - b)$ , where $a$ and $b$ can be any expressions.
Apply difference of squares pattern: Apply the difference of squares pattern to the given expression. $\newline$ Let $U = (x-2)^2$ and $V = (y+3)^2$ . Then the given expression can be written as $U^2 - V^2$ , which fits the pattern of a difference of squares.
Factor expression using difference of squares: Factor the expression using the difference of squares pattern. $\newline$ Using the pattern from Step $2$ , we can factor the expression as follows: $\newline$ $U^2 - V^2 = (U + V)(U - V)$ $\newline$ Substitute back U and V: $\newline$ $((x-2)^2 - (y+3)^2)((x-2)^2 + (y+3)^2)$
Verify factored expression: Verify that the factored expression is equivalent to the original expression. $\newline$ By expanding the factored expression, we should be able to get back to the original expression if our factoring is correct. However, this step is not necessary for choosing the correct pattern, so we can proceed to the answer.