Question

1. factor $100x^{2}+400x + 400$ using the perfect square trinomial method (if applicable).

a. $10x(x + 40)$
b. $(10x + 20)^{2}$
c. $(100x + 200)(x + 2)$
d. $(10x - 20)^{2}$

Explanation:

Step1: Identify perfect square form

Recall $(a+b)^2=a^2+2ab+b^2$

Step2: Match to given trinomial

$100x^2=(10x)^2$, $400=20^2$, $400x=2(10x)(20)$

Step3: Write factored form

$(10x+20)^2$

Answer:

b. $(10x + 20)^2$