Question

factor $0.04x^{2}+0.4x + 1$ using the perfect square trinomial method (if applicable).
a. $0.04(x^{2}+10)$
b. $(0.2x + 1)^{2}$
c. $(0.2x - 1)^{2}$
d. not a perfect square trinomial

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

factor $0.01x^{2}+0.2x + 1$ using the perfect square trinomial method (if applicable).
a. not a perfect square trinomial
b. $(0.1x + 1)^{2}$
c. $0.01(x^{2}+20)$
d. $(0.01x - 1)^{2}$

Explanation:

Problem 1: Factor $0.04x^2 + 0.4x + 1$

Step1: Identify square terms

$0.04x^2=(0.2x)^2$, $1=1^2$

Step2: Verify middle term

$2\times0.2x\times1=0.4x$, matches given term

Step3: Write perfect square

$(0.2x + 1)^2$

Problem 2: Factor $100x^2 + 400x + 400$

Step1: Identify square terms

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

Step2: Verify middle term

$2\times10x\times20=400x$, matches given term

Step3: Write perfect square

$(10x + 20)^2$

Problem 3: Factor $0.01x^2 + 0.2x + 1$

Step1: Identify square terms

$0.01x^2=(0.1x)^2$, $1=1^2$

Step2: Verify middle term

$2\times0.1x\times1=0.2x$, matches given term

Step3: Write perfect square

$(0.1x + 1)^2$

Answer:

1. b. $(0.2x + 1)^2$
2. c. $(10x + 20)^2$
3. b. $(0.1x + 1)^2$