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We want to factor the following expression:

9x^(4)+4y^(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: $\newline$ $9 x^{4}+4 y^{2}$ $\newline$ 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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Compare linear and exponential growth

Full solution

Q. We want to factor the following expression:

\newline

9 x^{4}+4 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.

Identify Structure: Identify the structure of the given expression. $\newline$ The given expression is $9x^{4} + 4y^{2}$ . We notice that both terms are perfect squares: $(3x^2)^2$ and $(2y)^2$ .
Recognize Factoring Pattern: Recognize the factoring pattern. The expression resembles the sum of two squares, which can be written as $A^2 + B^2$ , where $A = 3x^2$ and $B = 2y$ .
Determine Factoring Possibility: Determine if there is a factoring pattern for the sum of squares. $\newline$ The sum of squares does not factor over the real numbers using the patterns $(U+V)^2$ , $(U-V)^2$ , or $(U+V)(U-V)$ . These patterns apply to the difference of squares, not the sum of squares.
Conclude Pattern Usage: Conclude which pattern, if any, can be used. $\newline$ Since the sum of squares does not have a factoring pattern over the real numbers, we cannot use any of the given patterns to factor the expression $9x^{4} + 4y^{2}$ .

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Which pattern can we use to factor the expression?

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\newline

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(U+V)^{2}

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Question

We want to factor the following expression:

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Which pattern can we use to factor the expression?

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V

are either constant integers or single-variable expressions.

\newline

1

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(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

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Question

We want to factor the following expression:

\newline

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\newline

Which pattern can we use to factor the expression?

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V

are either constant integers or single-variable expressions.

\newline

1

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(U+V)^{2}

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Which pattern can we use to factor the expression?

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V

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\newline

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\newline

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Question

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