Factor the expression below completely, if possible. $x ^ { 4 } - 81 y ^ { 4 }$
A) $( x + 3 y ) ( x - 3 y ) \left( x ^ { 2 } + 9 y ^ { 2 } \right)$
B) $( x + 3 y ) ^ { 2 } ( x - 3 y ) ^ { 2 }$
C) $( x - 3 y ) ^ { 2 } \left( x ^ { 2 } + 9 y ^ { 2 } \right)$
D) $( x + 3 y ) ^ { 3 } ( x - 3 y )$
E)The expression is prime.

Question

Quizplus · Accepted Answer

The expression $x^4 - 81y^4$ is a difference of squares, which can be factored as $(x^2)^2 - (9y^2)^2$. This further factors into $(x^2 + 9y^2)(x^2 - 9y^2)$. The term $x^2 - 9y^2$ is also a difference of squares and can be factored as $(x + 3y)(x - 3y)$. Therefore, the complete factorization is $(x + 3y)(x - 3y)(x^2 + 9y^2)$.

Factor the Expression Below Completely, If Possible x4−81y4x ^ { 4 } - 81 y ^ { 4 }x4−81y4

Factor the Expression Below Completely, If Possible $x ^ { 4 } - 81 y ^ { 4 }$