a) \(2x^2y^2-\frac{4}{3}x^2y+2xy\)
b) \(2xy^2\left(x+5y\right)-4xy\left(5y+x\right)\)
\(=\left(x+5y\right)\left(2xy^2-4xy\right)\)
\(=2\left(x+5y\right)\left(xy^2-2xy\right)\)
c) \(25-4x^2-y^2+4xy\)
\(=25-\left(4x^2+y^2-4xy\right)\)
\(=5^2-\left[\left(2x\right)^2-2.2x.y+y^2\right]\)
\(=5^2-\left(2x-y\right)^2\)
\(=\left(5-2x+y\right)\left(5+2x-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y\right)+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(12y^3-3x^2y+12xy-12y\)
f) \(64x^4+y^4\)
\(=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2+4xy\right)\left(8x^2+y^2-4xy\right)\)
a) \(2x^2y^2-\frac{4}{3}x^2y+2xy\)
\(=xy\left(2xy-\frac{4}{3}x+2\right)\)
b) 2xy2.(x + 5y) - 4xy(5y + x)
= (5y + x)(2xy2 - 4xy)
= 2xy(5y + x)(y - 2)
c) 25 - 4x2 - y2 + 4xy
= 25 - (4x2 - 4xy + y2)
= 52 - (2x + y)2
= (5 - 2x - y)(5 + 2x + y)
d) x2 + 4x - 2xy - 4y +y2
= (x2 - 2xy + y2) + (4x - 4y)
= (x - y)2 + 4(x - y)
= (x - y)(x - y + 4)
e) 12y3 - 3x2y + 12xy - 12y
= 3y(4y2 - x2 + 4x - 4)
= 3y[4y2 - (x - 2)2]
= 3y(2y - x + 2)(2y + x - 2)
f) 64x4 + y4
= (8x2)2 + 16x2y2 + y4 - 16x2y2
= (8x2 + y2)2 - (4xy)2
= (8x2 + y2 - 4xy)(8x2 + y2 + 4xy)
d) x2 + 4x - 2xy - 4y + y2
<=> (x^2 - 2xy + y^2) + 4(x-y)
<=> (x-y)^2 + 4(x-y)
<=> (x-y)\(\left[\left(x+y\right)+4\right]\)
