Question

phân tích đa thức thành nhân tử

(x+3)^4+(x+5)^4-16

Answer 1

Đặt x+4=a

\(A=\left(a-1\right)^4+\left(a+1\right)^4-16\)

\(=\left(a^2-2a+1\right)^2+\left(a^2+2a+1\right)^2-16\)

\(=a^4+4a^2+1-4a^3+2a^2-4a+a^4+4a^2+1+4a^3+2a^2+4a-16\)

\(=2a^4+12a^2+2-16\)

\(=2\left(a^4+6a^2-7\right)\)

\(=2\left(a^2+7\right)\left(a^2-1\right)\)

\(=2\left[\left(x+4\right)^2+7\right]\left(x+3\right)\left(x+2\right)\)