We want to factor the following expression: 16x^(4)-25 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 form: Recognize the form of the expression. The expression 16x^(4)-25 is a difference of squares because it can be written as (4x^2)^2 - (5)^2.Apply difference of squares: Apply the difference of squares pattern. The difference of squares pattern is (U^2 - V^2) = (U + V)(U - V), where U and V are any expressions.Identify U and V: Identify U and V in the expression. In the expression 16x^(4)-25, U is 4x^2 and V is 5.Factor using difference of squares: Factor the expression using the difference of squares pattern. Using the pattern (U^2 - V^2) = (U + V)(U - V), we get (4x^2 + 5)(4x^2 - 5).Check the factored expression: Check the factored expression. (4x^2 + 5)(4x^2 - 5) when multiplied out should give us the original expression 16x^(4)-25. (4x^2 + 5)(4x^2 - 5) = 16x^4 - 20x^2 + 20x^2 - 25 = 16x^4 - 25, which is the original expression.

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We want to factor the following expression:

16x^(4)-25
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: $\newline$ $16 x^{4}-25$ $\newline$ 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

16 x^{4}-25

\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 form: Recognize the form of the expression. $\newline$ The expression $16x^{4}-25$ is a difference of squares because it can be written as $(4x^{2})^{2} - (5)^{2}$ .
Apply difference of squares: Apply the difference of squares pattern. $\newline$ The difference of squares pattern is $(U^2 - V^2) = (U + V)(U - V)$ , where $U$ and $V$ are any expressions.
Identify U and V: Identify U and V in the expression. $\newline$ In the expression $16x^{4}-25$ , U is $4x^2$ and V is $5$ .
Factor using difference of squares: Factor the expression using the difference of squares pattern. $\newline$ Using the pattern $(U^2 - V^2) = (U + V)(U - V)$ , we get $(4x^2 + 5)(4x^2 - 5)$ .
Check the factored expression: Check the factored expression. $\newline$ $(4x^2 + 5)(4x^2 - 5)$ when multiplied out should give us the original expression $16x^{4}-25$ . $\newline$ $(4x^2 + 5)(4x^2 - 5) = 16x^4 - 20x^2 + 20x^2 - 25 = 16x^4 - 25$ , which is the original expression.