Which of the following is equivalent to 2x^(2)(x-2) ? Choose 1 answer: (A) 2x^(3)-2 (B) 2x^(3)-2x^(2) (C) 2x^(3)-2x^(2)-2 (D) 2x^(3)-4x^(2)

Distribute First Term: We need to distribute the term 2x^2 to both terms inside the parentheses (x-2). Let's start with the first term: 2x^2 * x = 2x^(2+1) = 2x^3Distribute Second Term: Now, distribute 2x^2 to the second term inside the parentheses: 2x^2 * (-2) = -4x^2Combine Results: Combine the two results from the distribution to get the final expression: 2x^3 - 4x^2Compare with Answer Choices: Now, we compare the final expression with the answer choices to find the equivalent one: The final expression is 2x^3 - 4x^2, which matches with choice (D).

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Which of the following is equivalent to
2x^(2)(x-2) ?
Choose 1 answer:
(A)
2x^(3)-2
(B)
2x^(3)-2x^(2)
(C)
2x^(3)-2x^(2)-2
(D)
2x^(3)-4x^(2)

Which of the following is equivalent to $2 x^{2}(x-2)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2 x^{3}-2$ $\newline$ (B) $2 x^{3}-2 x^{2}$ $\newline$ (C) $2 x^{3}-2 x^{2}-2$ $\newline$ (D) $2 x^{3}-4 x^{2}$

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Full solution

Q. Which of the following is equivalent to

2 x^{2}(x-2)

\newline

Choose

1

answer:

\newline

(A)

2 x^{3}-2

\newline

(B)

2 x^{3}-2 x^{2}

\newline

(C)

2 x^{3}-2 x^{2}-2

\newline

(D)

2 x^{3}-4 x^{2}

Distribute First Term: We need to distribute the term $2x^2$ to both terms inside the parentheses $(x-2)$ . Let's start with the first term: $\newline$ $2x^2 \times x = 2x^{2+1} = 2x^3$
Distribute Second Term: Now, distribute $2x^2$ to the second term inside the parentheses: $\newline$ $2x^2 \times (-2) = -4x^2$
Combine Results: Combine the two results from the distribution to get the final expression: $2x^3 - 4x^2$
Compare with Answer Choices: Now, we compare the final expression with the answer choices to find the equivalent one: $\newline$ The final expression is $2x^3 - 4x^2$ , which matches with choice $(D)$ .