Question

factor $81x^{2}+162x + 81$ using the perfect square trinomial method (if applicable).
a. $(9x - 9)(9x + 9)$
b. $(9x + 9)^{2}$
c. $(81x + 81)^{2}$
d. $81(x^{2}+2x - 1)$

Explanation:

Step1: Identify perfect square form

A perfect square trinomial follows $a^2+2ab+b^2=(a+b)^2$.

Step2: Match terms to the form

For $81x^2+162x+81$:

• $a^2=81x^2 \implies a=9x$
• $b^2=81 \implies b=9$
• Verify $2ab=2(9x)(9)=162x$, which matches the middle term.

Step3: Write the factored form

Substitute $a$ and $b$ into $(a+b)^2$:
$(9x + 9)^2$

Answer:

b. $(9x + 9)^2$