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`