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a,(x-y)^2-2(x+y)+1 b, x^2-y^2+4x+4 c, 4x^2-y^2+8(y-2)
=(x-y-1)^2 =(x^2+4x+4)-y^2 =4x^2-y^2+8y-16
=(x+2)^2-y^2 =4x^2-(y^2-8y+16)
=(x+2-y)(x+2+y) =4x^2-(y-4)^2
a) (x+y)2-2(x+y)+1=(x+y-1)2
b) x2-y2+4x+4 = (x2+4x+4)-y2=(x+2)2-y2=(x+y+2)(x-y+2)
c)4x2-y2+8(y-2) = 4x2-(y2-8y+16) = (2x)2-(y-4)2=(2x+y-4)(2x-y+4)
d)x3-2x2+2x-4 = x2(x-2)+2(x-2) = (x-2)(x2+2)
e)xy-4+2x-2y=x(y+2) - 2(y+2) = (x-2)(y+2)
\(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(\Leftrightarrow\left(x+2\right)3x\)
1 ) \(x^2+xy+x=x\left(x+1+y\right)\)
2 ) \(3x^2\left(x-1\right)+5x\left(1-x\right)=3x^2\left(x-1\right)-5x\left(x-1\right)=\left(3x^2-5x\right)\left(x-1\right)\)
3 ) \(2x\left(x+y\right)-3x-3y=2x\left(x+y\right)-3\left(x+y\right)=\left(2x-3\right)\left(x+y\right)\)
4 ) \(x\left(x-y\right)+y\left(y-x\right)=x\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(x-y\right)=\left(x-y\right)^2\)
5 ) \(4x^2-36=4\left(x^2-9\right)=4\left(x+3\right)\left(x-3\right)\)
A . 5(x-y)-y(x-y)
=(x6-y)(5-y)
B . x^2 - xy - 8x+8y
=(x^2-xy)-(8x-8y))
=x(x-y) - 8(x-y)
C. x^2-10x+25 - y^2
=(x^2 - 10x + 25 ) - y^2
=(x-5)^2 - y^2
=(x-5+y)(x-5-y)
D . x^3 - 3x^2-4x+12
=(x^3 - 3x^2 ) - (4x - 12)
=x^2 (x-3)-4(x-3)
=(x^2-4)(x-3)
=(x+2)(x-2)(x-3)
D . 2x^2-2y^2- 6x-6y
=(2^x - 2y^2) - (6x+ 6y)
=2(x^2 - y^2) - 6(x+y)
=2(x+y)(x-y) - 6(x+y)
=2(x+y)(x-y-3)
E . x^3 - 3x^2 + 3x - 1
=(x-1)^3
D.x^2+3x+2
=x^2+2x+x+2
=(x^2+2x)+(x+2)
=x(x+2)+(x+2)
=(x+2)(x+1)
\(\left(1+x^2\right)^2-4x\left(1-x^2\right)=1+2x^{ }+x^4-4x+4x^3\)\(=\left(x^4+2x^3-x^2\right)+\left(2x^3+4x^2-2x\right)-x^2-2x+1=x^2\left(x^2+2x-1\right)+2x\left(x^2+x-1\right)-\left(x^2+2x-1\right)\)\(\left(x^2+2x-1\right)\left(x^2+2x-1\right)=\left(x^2+2x-1\right)^2\)
\(4x^2\left(x+y\right)-x-y\)
\(=4x^2\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(4x^2-1\right)\)
\(=\left(x+y\right)\left(2x-1\right)\left(2x+1\right)\)
\(16ty^2+6xt-9t-tx^2\)
\(=t.\left(16y^2+6x-9-x^2\right)\)
\(=t.\left[\left(4y\right)^2-\left(x^2-2.x.3+3^2\right)\right]\)
\(=t.\left[\left(4y\right)^2-\left(x-3\right)^2\right]\)
\(=t.\left(4y-x+3\right)\left(4y+x-3\right)\)
\(x^2-9xy+20y^2\)
\(=\left(x^2-4xy\right)-\left(5xy-20y^2\right)\)
\(=x.\left(x-4y\right)-5y\left(x-4y\right)\)
\(=\left(x-4y\right)\left(x-5y\right)\)