Factor the polynomial completely.
$x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$
A) The polynomial is prime.
B) $( x - 4 ) ^ { 2 } ( y - 3 ) ^ { 2 }$
C) (x y-16)(x y-9)
D) (x-4)(x+4)(y-3)(y+3)

Question

Factor the polynomial completely.
$x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$
A) The polynomial is prime.
B) $( x - 4 ) ^ { 2 } ( y - 3 ) ^ { 2 }$
C)  (x y-16)(x y-9) 
D)  (x-4)(x+4)(y-3)(y+3)

Quizplus · Accepted Answer

The given polynomial can be rearranged and factored by grouping: $x^2y^2 - 16y^2 - 9x^2 + 144$. This can be rewritten as $(x^2y^2 - 16y^2) - (9x^2 - 144)$, which simplifies to $y^2(x^2 - 16) - 9(x^2 - 16)$. Factoring out the common term $(x^2 - 16)$, we get $(x^2 - 16)(y^2 - 9)$. Further factoring each quadratic gives $(x - 4)(x + 4)(y - 3)(y + 3)$.

Factor the Polynomial Completely x2y2−9x2−16y2+144x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144x2y2−9x2−16y2+144

Factor the Polynomial Completely $x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$