Question

factor (100x^{2}+400x + 400) using the perfect square trinomial method (if applicable).
a. ((10x + 20)^{2})
b. (10x(x + 40))
c. ((10x - 20)^{2})
d. ((100x + 200)(x + 2))

factor (0.01x^{2}+0.14x + 0.49) using the perfect square trinomial method (if applicable).
a. (0.01(x^{2}+49))
b. ((0.1x + 0.7)^{2})
c. not a perfect square trinomial
d. ((0.1x - 0.7)^{2})

Explanation:

Step1: Identify perfect square terms

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

Step2: Verify middle term

Check $2\times10x\times20=400x$, matches.
Factor: $(10x+20)^2$

Step3: Identify perfect square terms

For $0.01x^2+0.14x+0.49$:
$0.01x^2=(0.1x)^2$, $0.49=0.7^2$

Step4: Verify middle term

Check $2\times0.1x\times0.7=0.14x$, matches.
Factor: $(0.1x+0.7)^2$

Answer:

1. a. $(10x + 20)^2$
2. b. $(0.1x + 0.7)^2$