Question

1. factor $0.04x^{2} + 0.28x + 0.49$ using the perfect square trinomial method (if applicable).

a. $0.04(x^{2} + 7x + 12.25)$
b. $(0.2x + 0.7)^{2}$
c. not a perfect square trinomial
d. $(0.2x - 0.7)^{2}$

1. factor $324x^{2} + 972x + 729$ using the perfect square trinomial method (if applicable).

a. $(18x + 27)^{2}$
b. $18x(x + 54)$
c. $(18x - 27)^{2}$
d. not a perfect square trinomial

Explanation:

First Problem: Factor $0.04x^2 + 0.28x + 0.49$

Step1: Identify square terms

$0.04x^2=(0.2x)^2$, $0.49=(0.7)^2$

Step2: Verify middle term

$2\times0.2x\times0.7=0.28x$, matches given term

Step3: Write perfect square

$(a+b)^2=a^2+2ab+b^2$, so substitute $a=0.2x, b=0.7$

Step1: Identify square terms

$324x^2=(18x)^2$, $729=(27)^2$

Step2: Verify middle term

$2\times18x\times27=972x$, matches given term

Step3: Write perfect square

$(a+b)^2=a^2+2ab+b^2$, so substitute $a=18x, b=27$

Answer:

b. $(0.2x + 0.7)^2$

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Second Problem: Factor $324x^2 + 972x + 729$