Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$32 x ^ { 4 } - 50 y ^ { 2 }$
A) $2 \left( 4 x ^ { 2 } - 5 y \right) ^ { 2 }$
B) $\left( 8 x ^ { 2 } + 10 y \right) \left( 4 x ^ { 2 } - 5 y \right)$
C) $2 \left( 4 x ^ { 2 } + 5 y \right) ^ { 2 }$
D) $2 \left( 4 x ^ { 2 } + 5 y \right) \left( 4 x ^ { 2 } - 5 y \right)$

Question

Quizplus · Accepted Answer

This polynomial can be factored using the difference of squares and then the difference of squares again. First, factor out a 2:
$$32x^4 - 50y^2 = 2(16x^4 - 25y^2)$$
Then, use the difference of squares:
$$2(4x^2 - 5y)(4x^2 + 5y)$$
Both of these factors can be factored again using the difference of squares. Therefore, the factored form is:
$$2(4x^2 - 5y)(2x+\sqrt{5}y)(2x-\sqrt{5}y)$$

Factor Completely 32x4−50y232 x ^ { 4 } - 50 y ^ { 2 }32x4−50y2

Factor Completely $32 x ^ { 4 } - 50 y ^ { 2 }$