7,x2-2xy+y2+3x-3y=(x-y)2+3(x-y)=(x-y)(x-y+3)
8,x4+4=(x4+4x2+4)-4x2=(x2+2)2-(2x)2=(x2-2x+2)(x2+2x+2)
9,4x(x+1)2-5x2(x+1)-4.(x+1)=(x+1)\(\left[4x\left(x+1\right)-5x^2-4\right]\)=(x+1)(4x2+4x-5x2-4)=(x+1)(-x2+4x-4)=-(x+1)(x-2)2
7: \(x^2-2xy+y^2+3x-3y\)
\(=\left(x-y\right)^2+3\cdot\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+3\right)\)
8: \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
9: \(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(4x^2+4x-5x^2-4\right)\)
\(=\left(x+1\right)\left(-x^2+4x-4\right)\)
\(=-\left(x+1\right)\left(x-2\right)^2\)
10: \(\left(1+2x\right)\left(1-2x\right)-\left(x+2\right)\left(x-2\right)\)
\(=1-4x^2-x^2+4\)
\(=-5x^2+5\)
\(=-5\left(x-1\right)\left(x+1\right)\)
