Question

Bài 3

a) \(\left(x^2+x\right)^2+4x^2+4x\)

b) \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

Answer 1

a)

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

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

\(=x(x+1)(x^2+x+4)\)

b) \(x(x+1)(x+2)(x+3)+1\)

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

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

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

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

Answer 2

c)

\((x+2)(x+3)(x+4)(x+5)-24\)

\(=[(x+2)(x+5)][(x+3)(x+4)]-24\)

\(=(x^2+7x+10)(x^2+7x+12)-24\)

Đặt \(x^2+7x+10=a\)

Khi đó biểu thức bằng:

\(a(a+2)-24=a^2+2a-24=a^2-4a+6a-24\)

\(=a(a-4)+6(a-4)=(a-4)(a+6)\)

\(=(x^2+7x+10-4)(x^2+7x+10+6)\)

\(=(x^2+7x+6)(x^2+7x+16)\)

\(=(x^2+x+6x+6)(x^2+7x+16)\)

\(=(x+1)(x+6)(x^2+7x+16)\)