Question

Bài 3.

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

b)\(\left(x^2+x\right)\left(x^2+x+1\right)-6\)

c)\(\left(x^2-4x\right)^2-8\left(x-4x\right)+15\)

Answer 1

a)

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

\(=[(x+2)(x+8)][(x+4)(x+6)]+16\)

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

\(=a(a+8)+16\) (Đặt \(x^2+10x+16=a\) )

\(=a^2+2.4.a+4^2=(a+4)^2\)

\(=(x^2+10x+16+4)^2\)

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

Answer 2

b) \((x^2+x)(x^2+x+1)-6\)

\(=(x^2+x)^2+(x^2+x)-6\)

\(=(x^2+x)^2-2(x^2+x)+3(x^2+x)-6\)

\(=(x^2+x)(x^2+x-2)+3(x^2+x-2)\)

\(=(x^2+x-2)(x^2+x+3)\)

\(=(x^2-x+2x-2)(x^2+x+3)\)

\(=[x(x-1)+2(x-1)](x^2+x+3)\)

\(=(x-1)(x+2)(x^2+x+3)\)

c)

\((x^2-4x)^2-8(x^2-4x)+15\)

\(=(x^2-4x)^2-3(x^2-4x)-5(x^2-4x)+15\)

\(=(x^2-4x)(x^2-4x-3)-5(x^2-4x-3)\)

\(=(x^2-4x-3)(x^2-4x-5)\)

\(=(x^2-4x-3)(x^2+x-5x-5)\)

\(=(x^2-4x-3)[x(x+1)-5(x+1)]=(x^2-4x-3)(x+1)(x-5)\)