Question

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Answer 1

Option A:

$\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}$

Solution:

Given expression $\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)$.

To find the product of the above expression:

$\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)$

First multiply first two factors with each term.

           $=(x^{4} \times 3 x^{3}- x^{4} \times 2 ) \left(4 x^{2}+5 x\right)$

Using exponent rule: $a^m \cdot a^n=a^{m+n}$

            $=(3 x^{7}- 2x^{4} ) \left(4 x^{2}+5 x\right)$

Now multiply these two factors with each term.

            $=3 x^{7} (4 x^{2}+5 x)- 2x^{4} \left(4 x^{2}+5 x\right)$

            $=(4 x^{2} \times 3 x^{7} +5 x \times 3 x^{7} )- \left(4 x^{2} \times 2x^{4}+5 x \times 2x^{4}\right)$

Using exponent rule: $a^m \cdot a^n=a^{m+n}$

            $=(12 x^{9} +15 x^{8} )- (8 x^{6}+10 x^{5})$

           $=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}$

$\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}$

Hence option A is the correct answer.