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a) \(7\left(3x-2\right)+y\left(3x-2\right)=\left(3x-2\right)\left(7+y\right)\)
b) \(x\left(y-x\right)-3\left(x-y\right)=x\left(y-x\right)+3\left(y-x\right)=\left(y-x\right)\left(x+3\right)\)
c) \(x^2-6xy+9y^2=\left(x-3y\right)^2\)
\(a,Sửa:x^2-xy-13x+13y=x\left(x-y\right)-13\left(x-y\right)=\left(x-13\right)\left(x-y\right)\\ b,=\left(x+y\right)^2-\left(2z\right)^2=\left(x+y-2z\right)\left(x+y+2z\right)\\ c,=\left(x^2-2x\right)-\left(3x-6\right)=x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)
\(a,=\left(2y^2-1\right)\left(2y^2+1\right)\\ b,=\left(x+y\right)^2-9=\left(x+y+3\right)\left(x+y-3\right)\)
Lời giải:
a. $4y^4-1=(2y^2)^2-1^2=(2y^2-1)(2y^2+1)$
b. $x^2+2xy-9+y^2=(x^2+2xy+y^2)-9$
$=(x+y)^2-3^2=(x+y-3)(x+y+3)$
\(x^2-2xy+x-2y=x\left(x-2y\right)+x-2y=\left(x-2y\right)\left(x+1\right)\)
\(3x^3+6x+3-3y^2=3\left[\left(x^2+2x+1\right)-y^2\right]=3\left[\left(x+1\right)^2-y^2\right]=3\left(x-y+1\right)\left(x+y+1\right)\)
a) \(=\left(3ax+3bx\right)-\left(4by+4ay\right)=3x\left(a+b\right)-4y\left(a+b\right)=\left(a+b\right)\left(3x-4y\right)\)
b) \(=3\left[\left(x^2-2xy+y^2\right)-4t^2\right]=3\left[\left(x-y\right)^2-4t^2\right]=3\left(x-y-2t\right)\left(x-y+2t\right)\)
c) Không phân tích được
x2-y2+6x+6y = (x2-y2)+(6x+6y) = (x-y)(x+y)+6(x+y) = (x-y-6)(x+y)
a) \(x^2-5xy+6y^2\)
\(=x^2-3xy-2xy+6y^2\)
\(=x\left(x-3y\right)-2y\left(x-3y\right)\)
\(=\left(x-2y\right)\left(x-3y\right)\)
b) \(16\left(x-1\right)^2-36y^2\)
\(=\left(4x-4\right)^2-\left(6y\right)^2\)
\(=\left(4x+6y-4\right)\left(4x-6y-4\right)\)
c) \(4\left(x+y\right)-12\left(x+y\right)^2\)
\(=\left(x+y\right)\left[4-12\left(x+y\right)\right]\)
\(=4\left(x+y\right)\left[1-3x-3y\right]\)