Question

1. factor $0.09x^{2}+0.6x + 1$ using the perfect square trinomial method (if applicable).

a. $0.09(x^{2}+\frac{20}{3}x+\frac{100}{9})$
b. $(0.3x + 1)^{2}$
c. $(0.3x - 1)^{2}$
d. not a perfect square trinomial

1. factor $0.01x^{2}+0.14x + 0.49$ using the perfect square trinomial method (if applicable).

a. $(0.1x + 0.7)^{2}$
b. not a perfect square trinomial
c. $(0.1x - 0.7)^{2}$
d. $0.01(x^{2}+49)$

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

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

Explanation:

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Problem 1:

Step1: Identify $a,b$ for trinomial

A perfect square trinomial has form $a^2+2ab+b^2=(a+b)^2$.
Here, $a^2=0.09x^2 \Rightarrow a=0.3x$, $b^2=1 \Rightarrow b=1$

Step2: Verify middle term

Check $2ab=2(0.3x)(1)=0.6x$, matches given middle term.

Step3: Write factored form

$(0.3x + 1)^2$

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Problem 2:

Step1: Identify $a,b$ for trinomial

For $a^2+2ab+b^2=(a+b)^2$, $a^2=0.01x^2 \Rightarrow a=0.1x$, $b^2=0.49 \Rightarrow b=0.7$

Step2: Verify middle term

$2ab=2(0.1x)(0.7)=0.14x$, matches given middle term.

Step3: Write factored form

$(0.1x + 0.7)^2$

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Problem 3:

Step1: Identify $a,b$ for trinomial

For $a^2+2ab+b^2=(a+b)^2$, $a^2=400x^2 \Rightarrow a=20x$, $b^2=400 \Rightarrow b=20$

Step2: Verify middle term

$2ab=2(20x)(20)=800x$, matches given middle term.

Step3: Write factored form

$(20x + 20)^2$

Answer:

1. b. $(0.3x + 1)^2$
2. a. $(0.1x + 0.7)^2$
3. a. $(20x + 20)^2$