Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$\left( 10 x y ^ { 2 } + x y \right) ^ { 2 }$$
A) $20 x ^ { 2 } y ^ { 4 } + 20 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$
B) $100 x ^ { 2 } y ^ { 4 } + x ^ { 2 } y ^ { 2 }$
C) $100 x ^ { 2 } y ^ { 4 } + 100 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$
D) $100 x ^ { 2 } y ^ { 4 } + 20 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$

Question

Quizplus · Accepted Answer

The square of a binomial $(a + b)^2$ is given by $a^2 + 2ab + b^2$. Applying this to $(10xy^2 + xy)^2$, we get $a^2 = (10xy^2)^2 = 100x^2y^4$, $2ab = 2 \cdot 10xy^2 \cdot xy = 20x^2y^3$, and $b^2 = (xy)^2 = x^2y^2$. Combining these gives $100x^2y^4 + 20x^2y^3 + x^2y^2$.

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