\(1.\)
\(a,\)
\(3x^2-6xy+3y^2\)
\(=3\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)^2\)
\(b,\)
\(12x^5y+24x^4y^2+12x^3y^3\)
\(=12x^3y\left(x^2+2xy+y^2\right)\)
\(=12x^3y\left(x+y\right)^2\)
\(c,\)
\(64xy-96x^2y+48x^3y-8x^4y\)
\(=8xy\left(8-12x+6x^2-x^3\right)\)
\(=8xy\left(2-x\right)^3\)
\(d,\)
\(54x^3+16y^3\)
\(=2\left(27x^3+8y^3\right)\)
\(=2\left[\left(3x\right)^3+\left(2y\right)^3\right]\)
\(=2\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)\)
\(2.\)
\(a,\)
\(x^2-2xy+y^2-4\)
\(=\left(x^2-2xy+y^2\right)-4\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
\(b,\)
\(-16x^2+8xy-y^2+49\)
\(=49-\left(16x^2-8xy+y^2\right)\)
\(=7^2-\left(4x-y\right)^2\)
\(=\left(7-4x+y\right)\left(7+4x-y\right)\)
\(3.\)
\(a,\)
\(x^6-x^4+2x^3+2x^2\)
\(=x^2\left(x^4-x^2+2x+2\right)\)
\(=x^2\left[x^2\left(x^2-1\right)+2\left(x+1\right)\right]\)
\(=x^2\left[x^2\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\right]\)
\(=x^2\left(x+1\right)\left[x^2\left(x-1\right)+2\right]\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
\(=x^2\left(x+1\right)\left(x^3+x^2-2x^2-2x+2x+2\right)\)
\(=x^2\left(x+1\right)\left[x^2\left(x+1\right)-2x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=x^2\left(x+1\right)\left(x+1\right)\left(x^2-2x+2\right)\)
\(=x^2\left(x+1\right)^2\left(x^2-2x+2\right)\)
\(b,\)
\(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\left(3x^2+y^2\right)\)
1:
a: =3(x^2-2xy+y^2)
=3(x-y)^2
b: \(=12x^3y\left(x^2+2xy+y^2\right)=12x^3y\left(x+y\right)^2\)
c: \(=8xy\left(8-12x+6x^2-x^3\right)\)
=8xy(2-x)^3
d: =2(27x^3+8y^3)
=2(3x+2y)(9x^2-6xy+4y^2)
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