Bài 2:
a: \(\left(3-xy^2\right)^2-\left(2+xy^2\right)^2\)
\(=\left(3-xy^2-2-xy^2\right)\left(3-xy^2+2+xy^2\right)\)
\(=5\left(-2xy^2+1\right)=-10xy^2+5\)
b: \(\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x^3-y^3-\left(x^3+y^3\right)\)
\(=x^3-y^3-x^3-y^3=-2y^3\)
c: \(\left(x-3\right)^3+\left(2-x\right)^3\)
\(=\left(x-3+2-x\right)\left[\left(x-3\right)^2+\left(x-3\right)\left(2-x\right)+\left(2-x\right)^2\right]\)
\(=-1\left(x^2-6x+9+2x-x^2-6+3x+x^2-4x+4\right)\)
\(=-1\left(x^2-7x+7\right)\)
\(=-x^2+7x-7\)
bài 3:
a: Sửa đề: \(8x^3yz+12x^2yz+6xyz+yz\)
\(=yz\left(8x^3+12x^2+6x+1\right)\)
\(=yz\left[\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3\right]\)
\(=yz\left(2x+1\right)^3\)
b: \(25\left(x+5\right)^2-9\left(x+7\right)^2\)
\(=\left(5x+25\right)^2-\left(3x+21\right)^2\)
\(=\left(5x+25-3x-21\right)\left(5x+25+3x+21\right)\)
\(=\left(2x+4\right)\left(8x+46\right)\)
\(=2\left(x+2\right)\cdot2\left(4x+23\right)\)
\(=4\left(x+2\right)\left(4x+23\right)\)
c: \(3x^2+4x-4\)
\(=3x^2+6x-2x-4\)
\(=3x\left(x+2\right)-2\left(x+2\right)\)
\(=\left(x+2\right)\left(3x-2\right)\)
d: \(2x\left(x-5\right)-x^2+5x\)
\(=2x\left(x-5\right)-x\left(x-5\right)\)
\(=\left(x-5\right)\left(2x-x\right)=x\left(x-5\right)\)
