25x^(2)-40 x+16 Which of the following is equivalent to the given expression? Choose 1 answer: (A) (5x-4)^(2) (B) (5x-2)(5x-8) (C) (5x+4)^(2) (D) (5x-4)(5x+4)

Finding the Product: The product of the coefficient of x^2 and the constant term is 25 * 16 = 400. We need two numbers that multiply to 400 and add up to -40. The numbers -20 and -20 fit this requirement because (-20) * (-20) = 400 and (-20) + (-20) = -40.Identifying the Numbers: Now we can write the quadratic expression as a perfect square because it follows the pattern of a^2 - 2ab + b^2, which is equivalent to (a - b)^2. Here, a is 5x and b is 4, so the expression 25x^2 - 40x + 16 can be written as (5x - 4)^2.Writing as a Perfect Square: We can check our factoring by expanding (5x - 4)^2 to verify that it gives us the original expression. Expanding (5x - 4)^2 gives us (5x - 4)(5x - 4) = 25x^2 - 20x - 20x + 16 = 25x^2 - 40x + 16, which matches the original expression.

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25x^(2)-40 x+16
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
(5x-4)^(2)
(B)
(5x-2)(5x-8)
(C)
(5x+4)^(2)
(D)
(5x-4)(5x+4)

$25 x^{2}-40 x+16$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $(5 x-4)^{2}$ $\newline$ (B) $(5 x-2)(5 x-8)$ $\newline$ (C) $(5 x+4)^{2}$ $\newline$ (D) $(5 x-4)(5 x+4)$

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Full solution

25 x^{2}-40 x+16

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

(5 x-4)^{2}

\newline

(B)

(5 x-2)(5 x-8)

\newline

(C)

(5 x+4)^{2}

\newline

(D)

(5 x-4)(5 x+4)

Finding the Product: The product of the coefficient of $x^2$ and the constant term is $25 \times 16 = 400$ . We need two numbers that multiply to $400$ and add up to $-40$ . The numbers $-20$ and $-20$ fit this requirement because $(-20) \times (-20) = 400$ and $(-20) + (-20) = -40$ .
Identifying the Numbers: Now we can write the quadratic expression as a perfect square because it follows the pattern of $a^2 - 2ab + b^2$ , which is equivalent to $(a - b)^2$ . Here, $a$ is $5x$ and $b$ is $4$ , so the expression $25x^2 - 40x + 16$ can be written as $(5x - 4)^2$ .
Writing as a Perfect Square: We can check our factoring by expanding $(5x - 4)^2$ to verify that it gives us the original expression. Expanding $(5x - 4)^2$ gives us $(5x - 4)(5x - 4) = 25x^2 - 20x - 20x + 16 = 25x^2 - 40x + 16$ , which matches the original expression.