Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$\left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right)$$
A) $8 x ^ { 2 } y ^ { 4 } - 80 x ^ { 2 } y ^ { 4 } - 20 x ^ { 2 }$
B) $16 x ^ { 2 } y ^ { 4 } - 100 x ^ { 2 }$
C) $8 x ^ { 2 } y ^ { 4 } - 20 x ^ { 2 }$
D) $16 x ^ { 2 } y ^ { 4 } - 80 x ^ { 2 } y ^ { 4 } - 100 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The rule for the product of the sum and difference of two terms is $(a + b)(a - b) = a^2 - b^2$. Applying this rule here, $a = 4xy^2$ and $b = 10x$, so the product is $(4xy^2)^2 - (10x)^2 = 16x^2y^4 - 100x^2$.

Multiply Using the Rule for the Product of the Sum (4xy2+10x)(4xy2−10x)\left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right)(4xy2+10x)(4xy2−10x)

Multiply Using the Rule for the Product of the Sum $\left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right)$