Question

factor y^2+8y+16-100t^2

Answer 1

Given

$y^2+8y+16-100t^2$

Find

Factorize the expression

Explanation

$\begin{gathered} y^2+8y+16-100t^2 \\ y^2+4y+4y+16-(10t)^2 \\ y(y+4)+4(y+4)-(10t)^2 \\ (y+4)(y+4)-(10t)^2 \\ (y+4)^2-(10t)^2 \end{gathered}$

now , we use the identity :

$a^2-b^2=(a+b)(a-b)$

so ,

$(y+4+10t)(y+4-10t)$

Final Answer

Hence , the required factor is

$(y+4+10t)(y+4-10t)$