Find the product.
-$$[ ( 4 x - y ) + 5 z ] [ ( 4 x - y ) - 5 z ]$$
A) $16 x ^ { 2 } + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$
B) $16 x ^ { 2 } - 8 x y + y ^ { 2 } - 25 z ^ { 2 }$
C) $16 x ^ { 2 } - 8 x y + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$
D) $16 x ^ { 2 } + y ^ { 2 } - 25 z ^ { 2 }$

Question

Quizplus · Accepted Answer

This problem uses the formula for the difference of squares, $a^2 - b^2 = (a + b)(a - b)$. Here, $a = 4x - y$ and $b = 5z$. Squaring $a$ gives $16x^2 - 8xy + y^2$, and squaring $b$ gives $25z^2$. Thus, the product is $16x^2 - 8xy + y^2 - 25z^2$.

Find the Product [(4x−y)+5z][(4x−y)−5z][ ( 4 x - y ) + 5 z ] [ ( 4 x - y ) - 5 z ][(4x−y)+5z][(4x−y)−5z]

Find the Product $[ ( 4 x - y ) + 5 z ] [ ( 4 x - y ) - 5 z ]$