select the correct answer.\nwhat is the completely factored form of this expression?\n$y^{2}-12y + 32$\na…

select the correct answer.\nwhat is the completely factored form of this expression?\n$y^{2}-12y + 32$\na. $(y + 4)(y + 8)$\nb. $(y - 4)(y - 8)$\nc. $(y + 18)(y + 2)$\nd. $(y - 18)(y - 2)$

select the correct answer.\nwhat is the completely factored form of this expression?\n$y^{2}-12y + 32$\na. $(y + 4)(y + 8)$\nb. $(y - 4)(y - 8)$\nc. $(y + 18)(y + 2)$\nd. $(y - 18)(y - 2)$

Answer

Answer:

B. $(y - 4)(y - 8)$

Explanation:

Step1: Analyze quadratic form

For a quadratic expression $ay^{2}+by + c$ (here $a = 1$, $b=-12$, $c = 32$), we need two numbers that multiply to $ac=32$ and add up to $b=-12$.

Step2: Find the two numbers

The two numbers are -4 and -8 since $(-4)\times(-8)=32$ and $-4+( - 8)=-12$.

Step3: Factor the expression

We can rewrite the middle - term and factor by grouping or directly write the factored form as $(y - 4)(y - 8)$.