Question

Phân tích đa thức thành nhân tử:

( x + 2 ) ( x + 4 ) ( x + 6 ) ( x + 8 ) + 16

Answer 1

Ta có:

 \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)

\(=\left(x^2+8x+2x+16\right)\left(x^2+6x+4x+24\right)+16\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+16+8\right)+16\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+16\right)+8\left(x^2+10x+16\right)+16\)

\(=\left(x^2+10x+16\right)^2+2.\left(x^2+10x+16\right).4+4^2\)

\(=\left(x^2+10x+16+4\right)^2=\left(x^2+10+20\right)^2\)

k nha!!

Answer 2

\(\text{( x + 2 ) ( x + 4 ) ( x + 6 ) ( x + 8 ) + 16}\)

\(\text{Phân tích thành nhân tử :}\)

\(\left(x^2+10x+20\right)^2\)

Answer 3

\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)

\(=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)

\(=\left(x^2+10x+16\right)\left(x^2+10+24\right)+16\)

\(=\left(x^2+10x+20-4\right)\left(x^2+10x+20+4\right)+16\)(*)

Đặt \(t=x^2+10x+20\)

(*)\(=\left(t-4\right)\left(t+4\right)+16\)

\(=t^2-16+16\)

\(=t^2\)

\(=\left(x^2+10x+20\right)^2\)

\(=\left(x^2+10x+20\right)\left(x^2+10x+20\right)\)