2x^(2)-50 Which of the following is equivalent to the given expression? Choose 1 answer: (A) 2x(x-25) (B) 2(x-5)(x+5) (c) -2(x-5)^(2) (D) -2(x+5)^(2)

Identify given expression: Identify the given expression and the task. We are given the expression 2x^(2)-50 and asked to find an equivalent expression among the choices provided.Factor out common factor: Factor out the common factor in the given expression. The expression 2x^(2)-50 has a common factor of 2 that can be factored out. 2(x^(2)-25)Recognize difference of squares pattern: Recognize the difference of squares pattern. The expression inside the parentheses, x^(2)-25, is a difference of squares since 25 is a perfect square (5^2). x^(2)-25 can be factored into (x-5)(x+5).Apply difference of squares factoring: Apply the difference of squares factoring. Now we factor x^(2)-25 using the difference of squares formula. 2(x^(2)-25) = 2(x-5)(x+5)Match factored expression with choices: Match the factored expression with the given choices. The factored expression 2(x-5)(x+5) matches choice (B).

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2x^(2)-50
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
2x(x-25)
(B)
2(x-5)(x+5)
(c)
-2(x-5)^(2)
(D)
-2(x+5)^(2)

$2 x^{2}-50$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2 x(x-25)$ $\newline$ (B) $2(x-5)(x+5)$ $\newline$ (C) $-2(x-5)^{2}$ $\newline$ (D) $-2(x+5)^{2}$

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Full solution

2 x^{2}-50

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

2 x(x-25)

\newline

(B)

2(x-5)(x+5)

\newline

(C)

-2(x-5)^{2}

\newline

(D)

-2(x+5)^{2}

Identify given expression: Identify the given expression and the task. $\newline$ We are given the expression $2x^{2}-50$ and asked to find an equivalent expression among the choices provided.
Factor out common factor: Factor out the common factor in the given expression. $\newline$ The expression $2x^{2}-50$ has a common factor of $2$ that can be factored out. $\newline$ $2(x^{2}-25)$
Recognize difference of squares pattern: Recognize the difference of squares pattern. $\newline$ The expression inside the parentheses, $x^{2}-25$ , is a difference of squares since $25$ is a perfect square ( $5^2$ ). $\newline$ $x^{2}-25$ can be factored into $(x-5)(x+5)$ .
Apply difference of squares factoring: Apply the difference of squares factoring. $\newline$ Now we factor $x^{2}-25$ using the difference of squares formula. $\newline$ $2(x^{2}-25) = 2(x-5)(x+5)$
Match factored expression with choices: Match the factored expression with the given choices. $\newline$ The factored expression $2(x-5)(x+5)$ matches choice (B).