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\(a,=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\\ b,=\left(x+y\right)\left(x-5\right)\\ c,=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2y\right)\left(x-y\right)\\ d,=x^2-2xy=x\left(x-2y\right)\\ e,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)
\(a,5x^2y-10xy^2=5xy\left(x-2y\right)\\ b,x^2+2xy+y^2-5x-5y=\left(x+y\right)^2-5\left(x+y\right)=\left(x+y\right)\left(x+y-5\right)\\ c,x^2-6x+8=\left(x^2-2x\right)-\left(4x-8\right)=x\left(x-2\right)-4\left(x-2\right)=\left(x-2\right)\left(x-4\right)\\ d,5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\)
a: \(=x\left(x-7y\right)+\left(x-7y\right)=\left(x-7y\right)\left(x+1\right)\)
\(a,=x\left(x-2\right)\\ b,=2b\left(x-3y\right)+a\left(x-3y\right)=\left(a+2b\right)\left(x-3y\right)\\ c,=x\left(x^2+2xy+y^2-4\right)=x\left[\left(x+y\right)^2-4\right]=x\left(x+y+2\right)\left(x+y-2\right)\\ d,=4-\left(x+y\right)^2=\left(2-x-y\right)\left(2+x+y\right)\\ đ,=5\left(x-y\right)\left(x+y\right)+3\left(x+y\right)^2=\left(x+y\right)\left(5x-5y+3x+3y\right)\\ =\left(x+y\right)\left(8x-2y\right)=2\left(4x-y\right)\left(x+y\right)\\ e,=3x\left(2xy-3\right)\\ b,=x\left(4x^2-4xy+y^2-4\right)=x\left[\left(2x-y\right)^2-4\right]=x\left(2x-y-2\right)\left(2x-y+2\right)\\ f,=\left(x+y\right)^2-z^2=\left(x+y-z\right)\left(x+y+z\right)\)
c) x2 + 2xy + y2 – xz – yz = (x + y)2 – z(x + y) = (x + y)(x + y – z)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
1. x2 + 2xy + y2 - xz - yz
= ( x2 +2xy + y2 ) - z ( x + y )
= ( x + y )2 - z ( x + y )
= ( x + y ) [( x + y ) - z ]
= ( x + y ) ( x + y - z )
1 x^2+2xy+y^2-xz-yz
=(x+y)^2-z(x+y)
=(x+y)(x+y-z)
2 (7x^2-14xy+7^2)-29z^2
=7(x^2-2xy+1)-29z^2
=7(x-1)^2-29z^2
=7(x-1)^2-25z^2-7z^2
=7(x-1-5)(x-1+5)-7z^2
=7(x-6)(x+4)-7z^2
=7((x+6)(x+4)-z^2)
3 5x^3-5x^2y+10x^2-10xy
=5x(x^2-xy+2x-2y)
4 5x^2-10xy+5y^2-20z^2
=5(x^2-2xy+y^2)-20z^2
=5(x+y)^2-20z^2
=5((x+y)^2-4z^2)
=5((x+y-2z)(x+y+2z))