Question

1. simplify \\((-10a^3b)(2a^2b)\\).

\\(-8a^5b^2\\)

\\(-8a^6b\\)

\\(-20a^6b^2\\)

\\(-20a^5b^2\\)

Explanation:

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<reasoning>

Group coefficients and variables

\[
(-10 \cdot 2) \cdot (a^3 \cdot a^2) \cdot (b \cdot b)
\]

Multiply coefficients

\[
-10 \cdot 2 = -20
\]

Apply exponent rules to variables

\[

$$\begin{aligned} a^3 \cdot a^2 &= a^{3+2} = a^5 \\ b^1 \cdot b^1 &= b^{1+1} = b^2 \\ (-10a^3b)(2a^2b) &= -20a^5b^2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(-8a^5b^2\)</mcq-option>
<mcq-option>(B) \(-8a^6b\)</mcq-option>
<mcq-option>(C) \(-20a^6b^2\)</mcq-option>
<mcq-correct>(D) \(-20a^5b^2\)</mcq-correct>
</answer>

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Answer:

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</pre_analysis>

<reasoning>

Group coefficients and variables

\[
(-10 \cdot 2) \cdot (a^3 \cdot a^2) \cdot (b \cdot b)
\]

Multiply coefficients

\[
-10 \cdot 2 = -20
\]

Apply exponent rules to variables

\[

$$\begin{aligned} a^3 \cdot a^2 &= a^{3+2} = a^5 \\ b^1 \cdot b^1 &= b^{1+1} = b^2 \\ (-10a^3b)(2a^2b) &= -20a^5b^2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(-8a^5b^2\)</mcq-option>
<mcq-option>(B) \(-8a^6b\)</mcq-option>
<mcq-option>(C) \(-20a^6b^2\)</mcq-option>
<mcq-correct>(D) \(-20a^5b^2\)</mcq-correct>
</answer>

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