Question

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Answer 1

Option D:

$\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7$

Solution:

Given expression is $\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)$.

To find the product of the expression:

$\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)$

Multiply each term of the first term with each term of the 2nd term.

           $=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)$

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

           $=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)$

           $=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7$

Arrange the terms with same power.

           $=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7$

           $=8 y^{4}+25 y^{3}+60 y^{2}+10y+7$

Hence option D is the correct answer.

$\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7$