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\(14x^2y-21xy^2+28x^2y=7xy\left(2x-3y+4x\right)=21xy\left(2x-y\right)\)
\(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
\(10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)
\(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)
a,=5xy(x-2y)
b,=3(x+3)+(x-3)(x+3)
=(x+3)+x
c=xy(x-y)+z(x-y)
=(x-y)(xy+z)
d=7xy(2x-3y+4xy)
e,=x(x+y)-5(x+y)
= (x+y)(x-5)
f, =10x(x-y)+8(x-y)
=(x-y)(10x+8)
g,=(3x+1-x+1)(3x+1+x+1)
=2x(4x+2)
h,=x^2-3x-2x+6
= x(x-3)-2(x-3)
=(x-3)(x-2)
d: \(=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
a) x (x + y) - 3x - 3y
⇔ x ( x + y ) - 3 ( x + y )
⇔ ( x - 3 ) ( x + y )
b) x (x + y) - 5x - 5y
⇔ x ( x + y ) - 5 ( x + y )
⇔ ( x - 5 ) ( x + y )
c) x (x + y) - 7x - 7y
⇔ x ( x + y ) - 7 ( x + y )
⇔ ( x - 7 ) ( x + y )
d) x2 (x - y) + 2x - 2y
⇔ x\(^2\) ( x - y ) + 2 ( x - y )
⇔ ( x\(^2\) - 2 ) ( x - y )
a) \(x\left(x+y\right)-3x-3y=x\left(x+y\right)-3\left(x+y\right)=\left(x+y\right)\left(x-3\right)\)
b)\(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
c) \(x\left(x+y\right)-7x-7y=x\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(x-7\right)\)
d) \(x^2\left(x-y\right)+2x-2y=x^2\left(x-y\right)+2\left(x-y\right)=\left(x-y\right)\left(x^2+2\right)\)
\(1,=3xy\left(x^2+2xy+y^2\right)=3xy\left(x+y\right)^2\\ 2,=7xy\left(2x-3y+4xy\right)\\ 3,=\left(x-1\right)\left(x^2-4\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\\ 4,=\left(x-y\right)\left(10x+8\right)=2\left(5x+4\right)\left(x-y\right)\\ 5,=\left(b-c\right)\left(8a-6b\right)=2\left(4a-3b\right)\left(b-c\right)\\ 6,=\left(x-1\right)\left(x^2-16\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\\ 7,=x\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(x+5\right)\\ 8,=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\\ 9,=\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\\ 10,=\left(x-1\right)^2-4y^2=\left(x-2y-1\right)\left(x+2y-1\right)\)
c: \(x^2-10x+21=\left(x-3\right)\left(x-7\right)\)
a: \(x^2y+xy^3-xy-y^3\)
\(=xy\left(x-1\right)+y^3\left(x-1\right)\)
\(=y\left(x-1\right)\left(x+y^2\right)\)
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