Question

Phân tích đa thức thành nhân tử :

a, (3x+1)²-(x+1)²

b, x³+y³+z^3-3xyz

Tính nhanh :

87³+73²-27²-13²

Help

Answer 1

Bài 1:

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

\(=2x\left(4x+2\right)=4x\left(2x+1\right)\)

b, \(x^3+y^3+z^3-3xyz\)

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

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

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

Answer 2

\(87^2+73^2-27^2-13^2=\left(87^2-13^2\right)+\left(73^2-27^2\right)=74.100+46.100=100\cdot\left(74+46\right)=12000\)