Question

Phân tích thành nhân tử: \(\left(x^2-7x+12\right)\left(x^2-15x+56\right)-60\)

Answer 1

\(=\left(x^2-11x+26+4x-14\right)\left(x^2-11x+26-4x+14\right)+16\left(x^2-7x+12\right)-60\)

\(=\left(x^2-11x+26\right)^2-\left(4x-14\right)^2+\left(16x^2-2\cdot4\cdot14x+14^2\right)-64\)

\(=\left(x^2-11x+18\right)\left(x^2-11x+34\right)-\left(4x+14\right)^2+\left(4x+14\right)^2\)

\(=\left(x^2-2x-9x+18\right)\left(x^2-11x+34\right)\)

\(=\left(x-2\right)\left(x-9\right)\left(x^2-11x+34\right)\)