Question

Phân tích thành nhân tử:

\(\left(x^2+8x-34\right)^2-\left(3x^2-8x+2\right)^2\)

Answer 1

\(\left(x^2+8x-34\right)^2-\left(3x^2-8x+2\right)^2\\=\left(x^2+8x-34+3x^2-8x+2\right)\left(x^2+8x-34-3x^2+8x-2\right)\\ =\left(4x^2-32\right)\left(-2x^2+16x-36\right)\\ =4\left(x^2-8\right).\left(-2\right)\left(x^2-8x+18\right) \\ =-8\left(x+\sqrt{8}\right)\left(x-\sqrt{8}\right)\left(x^2-8x+18\right)\)

Answer 2

\(\left(x^2+8x-34\right)^2-\left(3x^2-8x+2\right)^2\)

\(=\left(x^2+8x-34-3x^2+8x-2\right)\left(x^2+8x-34+3x^2-8x+2\right)\)

\(=\left(-2x^2+16x-36\right)\left(4x^2-32\right)\)