Question

factor ( 625x^2 + 2500x + 2500 ) using the perfect square trinomial method (if applicable).

a. ( (25x - 50)^2 )
b. ( 25x(x + 100) )
c. ( (25x + 50)^2 )
d. not a perfect square trinomial

factor ( 484x^2 + 968x + 484 ) using the perfect square trinomial method (if applicable).

a. ( (22x + 22)^2 )
b. ( 22x(x + 44) )
c. ( (22x - 22)^2 )
d. not a perfect square trinomial

Explanation:

First Problem: Factor $625x^2 + 2500x + 2500$

Step1: Identify $a$ and $c$ roots

$a=\sqrt{625x^2}=25x$, $c=\sqrt{2500}=50$

Step2: Verify middle term

$2ac=2(25x)(50)=2500x$, matches given term

Step3: Write perfect square

$(a+c)^2=(25x+50)^2$

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Second Problem: Factor $484x^2 + 968x + 484$

Step1: Identify $a$ and $c$ roots

$a=\sqrt{484x^2}=22x$, $c=\sqrt{484}=22$

Step2: Verify middle term

$2ac=2(22x)(22)=968x$, matches given term

Step3: Write perfect square

$(a+c)^2=(22x+22)^2$

Answer:

c. $(25x + 50)^2$