Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$\left( a ^ { n } + 3 b ^ { n } \right) ^ { 2 }$$
A) $a ^ { 2 n } + 6 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$
B) $a ^ { n } + 6 a ^ { n } b ^ { n } + 9 b ^ { n }$
C) $a ^ { n + 2 } + 6 a ^ { n } b ^ { n } + 9 b ^ { n + 2 }$
D) $a ^ { 2 n } + 3 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$

Question

Quizplus · Accepted Answer

The square of a binomial $(x + y)^2$ is given by $x^2 + 2xy + y^2$. Applying this rule to $(a^n + 3b^n)^2$, we get $a^{2n} + 2(a^n)(3b^n) + (3b^n)^2$, which simplifies to $a^{2n} + 6a^nb^n + 9b^{2n}$.

Multiply Using One of the Rules for the Square of a Binomial