Question

Product of $6a^2–7b+5ab$ and $2ab$ is

• A. (a) $12a^{3}b–14a{b}^2+10ab$
• B. (b) $12a^{3}b–14a{b}^2+10a^2{b}^2$
• C. (c) $6a^2–7b+7ab$
• D. (d) $12a^{2}b–7a{b}^2+10ab$

Answer 1

The correct option is B

(b) $12a^{3}b–14a{b}^2+10a^2{b}^2$

Step 1. Determine the product of $6a^2–7b+5ab$ and $2ab$.

Use the distributive property of multiplication, $a\left(b+c+d\right)=ab+ac+ad$

$\begin{array}{rcl}\left(6a^2–7b+5ab\right)2ab& =& \left(6a^2\right)\left(2ab\right)-\left(7b\right)\left(2ab\right)+\left(5ab\right)\left(2ab\right)\\ & =& \left(6·2\right)\left(a^2·ab\right)-\left(7·2\right)\left(b·ab\right)+\left(5·2\right)\left(ab·ab\right)\\ & =& 12\left(a^{2+1}b\right)-14\left(a{b}^{1+1}\right)+10\left(a^{1+1}{b}^{1+1}\right)\mathbf{}\mathbf{[}\mathbf{\because }{\mathit{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\mathbf{=}{\mathit{a}}^{\mathbf{m}}\mathbf{·}{\mathit{a}}^{\mathbf{n}}\mathbf{]}\\ & =& 12a^{3}b-14a{b}^2+10a^2{b}^2\end{array}$

Hence, the product of $6a^2–7b+5ab$ and $2ab$ is $12a^{3}b-14a{b}^2+10a^2{b}^2$. The correct option is (b).