Question

factor $625x^{2} + 1250x + 625$ using the perfect square trinomial method (if applicable).
a. not a perfect square trinomial
b. $(25x + 25)^{2}$
c. $(25x - 25)^{2}$
d. $25x(x + 50)$

Explanation:

Step1: Identify square terms

First term: $625x^2=(25x)^2$, last term: $625=25^2$

Step2: Verify middle term

Check if $2\times25x\times25=1250x$, which matches the given middle term.

Step3: Apply perfect square formula

Use $(a+b)^2=a^2+2ab+b^2$, where $a=25x$, $b=25$.
Result: $(25x + 25)^2$

Answer:

b. $(25x + 25)^2$