Question

factor $0.09x^{2}+0.18x + 0.09$ using the perfect square trinomial method (if applicable).
a. $(0.3x + 0.3)^{2}$
b. not a perfect square trinomial
c. $0.01(x^{2}+2x + 1)$
d. $(0.3x - 0.3)^{2}$

factor $400z^{2}+1200z + 900$ using the perfect square trinomial method (if applicable).
a. $(20z - 30)^{2}$
b. not a perfect square trinomial
c. $(20z + 30)^{2}$
d. $20z(z + 60)$

Explanation:

First Problem: Factor $0.09x^2 + 0.18x + 0.09$

Step1: Identify square terms

$0.09x^2=(0.3x)^2$, $0.09=(0.3)^2$

Step2: Verify middle term

$2\times0.3x\times0.3=0.18x$, matches given term

Step3: Write perfect square form

$(0.3x+0.3)^2$

Step1: Identify square terms

$400z^2=(20z)^2$, $900=(30)^2$

Step2: Verify middle term

$2\times20z\times30=1200z$, matches given term

Step3: Write perfect square form

$(20z+30)^2$

Answer:

a. $(0.3x + 0.3)^2$

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Second Problem: Factor $400z^2 + 1200z + 900$