Question

Factor the difference of squares: x^6-16x^4-81x^2+1296

Answer 1

x^6-16x^4-81x^2+1296


x^4(x^2-16)-81(x^2-16)


(x^4-81)(x^2-16)


(x^2-9)(x^2+9)(x^2-16)


(x-3)(x+3)(x^2+9)(x^2-16)


(x-3)(x+3)(x^2+9)(x-4)(x+4)



So x^6-16x^4-81x^2+1296 completely factors to (x-3)(x+3)(x^2+9)(x-4)(x+4)


In other words, x^6-16x^4-81x^2+1296 = (x-3)(x+3)(x^2+9)(x-4)(x+4)