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\(\left(ab+1\right)^2-\left(a+b\right)^2=\left(ab+1+a+b\right)\left(ab+1-a-b\right).\)
\(=\left(a+1\right)\left(b+1\right)\left(a-1\right)\left(b-1\right)\)
\\(x^2-2x-4y^2-4y=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)=\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\left(x+1+2y+1\right)\left(x+1-2y-1\right)=\left(x+2y+2\right)\left(x-2y\right)\)
\(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x+x+2\right)\left(x^2+x-x-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
\(x^2-2x-4y^2-4y=\left(x^2-2x+1\right)-\left(4y^2-4y+1\right)\)
\(=\left(x-1\right)^2-\left(2y-1\right)^2=\left(x-1+2y-1\right)\left(x-1-2y+1\right)\)
\(=\left(x-2y\right)\left(x+2y-2\right)\)
\(x^2-4y^2+4y-1=x^2-\left(2y-1\right)^2=\left(x+2y-1\right)\left(x-2y+1\right)\)
\(x^4+3x^3-9x-9\)
\(=x^4-9+3x^3-9x\)
\(=\left(x^2-3\right)\left(x^2+3\right)+3x\left(x^2-3\right)\)
\(=\left(x^2-3\right)\left(x^2+3+3x\right)\)
\(4x^3-13x^2+9x-18 \)
\(=4x^2\left(x-3\right)-x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(4x^2-x+6\right)\)
\(4x+by+4y+bx=\) \(\left(4x+4y\right)+\left(by+bx\right)\)
\(=\) \(4\left(x+y\right)+b\left(x+y\right)\)
\(=\left(4+b\right)\left(x+y\right)\)
\(2x^2+xy-2x-y=\) \(\left(2x^2+xy\right)-\left(2x+y\right)\)
\(=x\left(2x+y\right)-\left(2x+y\right)\)
\(=\left(x-1\right)\left(2x+y\right)\)
= ( X2 - 2X+ 1) -4Y2
= (X-1)2 - (2Y)2
= (X-1-2Y)(X-1+2Y)
d,
\(a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
Vậy..
e
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\left(x-2y-2\right)\left(x+2y\right)\)
\(x^2-2x-4y^2-4y=\left(x^2-4y\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x-2y-2\right)\left(x+2y\right)\)
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\left(x+1+2y+1\right)\left(x+1-2y-1\right)\)
\(=\left(x+2y+2\right)\left(x-2y\right)\)