\(\left(xy+1\right)^2-\left(x+y\right)^2=\left(xy+1-x-y\right)\left(xy+1+x+y\right)\)
\(=\left[y\left(x-1\right)-\left(x-1\right)\right]\left[x\left(y+1\right)+\left(y+1\right)\right]\)
\(=\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)\)
b.
\(\left(x+y\right)^3-\left(x-y\right)^3=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x-y\right)\left(x+y\right)+\left(x-y\right)^2\right]\)
\(=2y\left(3x^2+y^2\right)\)
c.
\(3x^4y^2+3x^3y^2+3xy^2+3y^2=3x^3y^2\left(x+1\right)+3y^2\left(x+1\right)\)
\(=3y^2\left(x+1\right)\left(x^3+1\right)\)
\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)
d.
\(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)
\(=4x^2-8x+4-\left(4y^2-8ay+4a^2\right)\)
\(=4\left[\left(x-1\right)^2-\left(y-a\right)^2\right]\)
\(=4\left(x-1+y-a\right)\left(x-1-y+a\right)\)
a)
\(=\left(xy+1-x-y\right)\left(xy+1+x+y\right)\)
b)
\(=x^3+3x^2y+3xy^2+y^3-\left(x^3-3x^2y+3xy^2-y^3\right)\)
\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3\)
\(=x^3-x^3+3x^2y+3x^2y+3xy^2-3xy^2+y^3+y^3\)
\(=6x^2y+2y^3=2y\left(3x^2+y^2\right)\)
c)
\(=3y^2\left(x^4+x^3+x+1\right)\)
\(=3y^2\left[x^3\left(x+1\right)+\left(x+1\right)\right]\)
\(=3y^2\left(x+1\right)\left(x^3+1\right)\)
\(=3y^2\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)=3y^2\left(x^2+2x+1\right)\left(x^2-x+1\right)\)
d)
\(=4x^2-4y^2-8x+8ay-4a^2+4\)
\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)
\(=\left(2x-2\right)^2-\left(2y-2a\right)^2\)
\(=\left(2x-2-2y+2a\right)\left(2x-2+2y-2a\right)\)
\(=4\left(x-1-y+a\right)\left(x-1+y-a\right)\)
a, (xy+1) mũ 2 -(x+y) mũ 2 =(xy+1-x-y).(xy+1+x+y) =[(xy-x)+(1-y)].[(xy+x)+(1+y)]=[x.(y-1)-(y-1)].[x.(y+1)-(y+1)]=(y-1).(x-1).(y+1).(x-1)=(x-1).[(y-1).(x-1)] dài thế :))
