Question

1. factor (400x^{2}+800x + 400) using the perfect square trinomial method (if applicable).

a. ((20x - 20)^{2})
b. ((20x + 20)^{2})
c. not a perfect square trinomial
d. (20x(x + 40))

Explanation:

Step1: Identify perfect square form

A perfect square trinomial follows $a^2+2ab+b^2=(a+b)^2$.

Step2: Match terms to the form

$400x^2=(20x)^2$, so $a=20x$; $400=20^2$, so $b=20$.
Check $2ab=2(20x)(20)=800x$, which matches the middle term.

Step3: Write factored form

Substitute $a$ and $b$ into $(a+b)^2$: $(20x+20)^2$

Answer:

b. $(20x + 20)^2$