Question

Phân tích các đa thức thành nhân tử: a) (x + y)3 + (x – y)3 . b) (x + 1)(x + 2)(x + 3)(x + 4) – 3.

Answer 1

b: Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-3\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-3\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+21\)

\(=\left(x^2+5x+3\right)\left(x^2+5x+7\right)\)

Answer 2

a, \(\left(x+y\right)^3+\left(x-y\right)^3=\left(x+y+x-y\right)\left[\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)

\(=2x\left(x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2\right)=2x\left(x^2+3y^2\right)\)

b, \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-3=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-3\)

Đặt \(x^2+5x+5=t\)

\(\left(t-1\right)\left(t+1\right)-3=t^2-4=\left(t-2\right)\left(t+2\right)\)

Theo cách đặt \(\left(x^2+5x+3\right)\left(x^2+5x+7\right)\)

Answer 3

a)\(\left(x+y\right)^3+\left(x-y\right)^3\)
\(=\left(x+y+x-y\right)\left[\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=2x\left(x^2+2xy+y^2-x^2+xy-xy+y^2+x^2-2xy+y^2\right)\)
\(=2x\left(x^2+3y^2\right)\)

Answer 4

a:\(\left(x+y\right)^3+\left(x-y\right)^3\)

\(=\left(x+y+x-y\right)\left(x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2\right)\)

\(=2x\cdot\left(3y^2+x^2\right)\)