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\(\left(2x^2+4xz-6xy\right)-\left(xy+2yz-3y^2\right)+\left(2z^2+xz-3yz\right)\)
\(2x\left(x+2z-3y\right)-y\left(x+2z-3y\right)+z\left(2z+x-3y\right)\)
\(\left(x+2z-3y\right)\left(2x-y+z\right)\)
a) \(x^2+6x+8\)
\(=\left(x^2-2x\right)-4x+8\)
\(=x\left(x-2\right)-4\left(x-2\right)\)
\(\left(x-2\right)\left(x-4\right)\)
b) \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
a) x2 - 6x + 8
= x2 -2x - 4x +8
= x( x-2) -4( x-2)
= ( x-2)(x-4)
a) \(x^2-3xy+x-3y=x\left(x-3y\right)+\left(x-3y\right)=\left(x-3y\right)\left(x+1\right)\)
b) \(x^2-6x-y^2+9=x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
c) \(7x^3y-14x^2y+7xy=7xy\left(x^2-2x+1\right)=7xy\left(x-1\right)^2\)
\(x^2-3xy+x-3y=\left(x^2+x\right)-\left(3xy+3y\right)=x\left(x+1\right)-3y\left(x+1\right)=\left(x+1\right)\left(x-3y\right)\)
\(x^2-6x-y^2+9=\left(x^2-2.x.3+3^2\right)-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
\(7x^3y-14x^2y+7xy=\left(7x^3y-7x^2y\right)-\left(7x^2y-7xy\right)=7x^2y.\left(x-1\right)-7xy.\left(x-1\right)\)
\(=\left(x-1\right).\left(7x^2y-7xy\right)=7xy.\left(x-1\right).\left(x-1\right)=7xy.\left(x-1\right)^2\)
a. \(2a^2+5ab-3b^2-7b-2\)
\(=\left(2a^2+6ab+2a\right)-\left(ab+3b^2+b\right)-\left(2a+6b+2\right)\)
\(=2a\left(a+3b+1\right)-b\left(a+3b+1\right)-2\left(a+3b+1\right)\)
\(=\left(2a-b-2\right)\left(a+3b+1\right)\)
b. \(2x^2-7xy+x+3y^2-3y\)
\(=\left(2x^2-xy\right)-\left(6xy-3y^2\right)+\left(x-3y\right)\)
\(=x\left(2x-y\right)-3y\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y+1\right)\)
c. \(6x^2-xy-2y^2+3x-2y\)
\(=\left(6x^2+3xy\right)-\left(4xy-2y^2\right)+\left(3x-2y\right)\)
\(=3x\left(2x+y\right)-2y\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y+1\right)\)
a) x4 + 6x2y + 9y2 - 1
= (x2 + 3y)2 - 1
= (x2 + 3y + 1)(x2 + 3y - 1)
b) 2x2 + 3x - 5
= 2x2 - 2x + 5x - 5
= 2x(x - 1) + 5(x - 1)
= (2x + 5)(x - 1)
c) x2 - 7xy + 10y2
= x2 - 2xy - 5xy + 10y2
= x(x - 2y) - 5y(x - 2y)
= (x - 5y)(x - 2y)
a, \(x^4+6x^2y+9y^2-1\)
\(=\left(x^2+3y\right)^2-1\)
\(=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)
b, \(2x^2+3x-5\)
\(=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
c, \(x^2-7xy+10y^2\)
\(=x^2-4xy+4y^2-3xy+6y^2\)
\(=\left(x-2y\right)^2-3y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
\(x^2+3x+3y+xy=x^2+xy+3x+3y=x.\left(x+y\right)+3.\left(x+y\right)\) \(=\left(x+3\right)\left(x+y\right)\)
\(x^2+5x^2+6x=x^2+x+5x^2+5x=x\left(x+1\right)+5x\left(x+1\right)\) \(=\left(x+5x\right)\left(x+1\right)=6x\left(x+1\right)\)
a)\(x^2+3x+3y+xy\)
\(=x\left(x+y\right)+3\left(x+y\right)\)
\(=\left(x+3\right)\left(x+y\right)\)
\(=6x^2-9xy+2xy-3y^2\)
=3x(2x-y)+y(2x-y)
=(2x-y)(3x+y)