Question

Phân tích đa thức thành nhân tử:

a)\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)

b)\(x^7+x^2+1\)

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

d)\(\left(x^2+8x+7\right)\left(x+3\right)\left(x+5\right)+15\)

e)\(x^2-2xy+y^2+3x-3y-10\)

Answer 1

c: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

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

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

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

d: \(=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+120\)

\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

\(=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)

e: \(x^2-2xy+y^2+3x-3y-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

\(=\left(x-y+5\right)\left(x-y-2\right)\)