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1A:
a: \(x^3+2x=x\left(x^2+2\right)\)
b: \(3x-6y=3\left(x-2y\right)\)
c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)
\(=5\left(x+3y\right)\left(1-3x\right)\)
d: \(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+3\right)\)
1A. a. x(x2+2)
b. 3(x-2y)
c. 5(x+3y)(1-3x)
d. (x-y) (3-5x)
1B. a. 2x(2x-3)
b.xy(x2-2xy+5)
c. 2x(x+1)(x+2)
d. 2x(y-1)+2y(y-1)=2(y-1)(x-y)
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a) \(=6x^2y^2\left(6xy-7\right)\)
b) \(=3xy\left(x^3y+5x-6\right)\)
c) \(=\left(ax+ab\right)-\left(bx+x^2\right)=a\left(b+x\right)-x\left(b+x\right)=\left(a-x\right)\left(b+x\right)\)
d) \(=3\left(2x-1\right)-\left(2x-1\right)^2=\left(2x-1\right)\left(3-2x+1\right)=\left(2x-1\right)\left(4-2x\right)=2\left(2x-1\right)\left(2-x\right)\)
\(a,=6x^2y^2\left(6xy-7\right)\\ b,=3xy\left(x^3y+5x-6\right)\\ c,=x\left(a-x\right)-b\left(a-x\right)=\left(x-b\right)\left(a-x\right)\\ d,=3\left(2x-1\right)-\left(2x-1\right)^2=\left(2x-1\right)\left(3-2x+1\right)=2\left(2-x\right)\left(2x-1\right)\)
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a: \(=\left(2x+y\right)^2-3^2=\left(2x+y+3\right)\left(2x+y-3\right)\)
b: =3x(x-y)-(x-y)=(x-y)(3x-1)
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`a)(x+2)^2+2(x^2-4)+(x-2)^2`
`=(x+2)^2+2(x-2)(x+2)+(x-2)^2`
`=(x+2+x-2)^2=(2x)^2=4x^2`
`b)x^2-x+1/4`
`=x^2-2.x .1/2+1/4=(x-1/2)^2`
`c)(x+y)^3-(x-y)^3`
`=(x+y-x+y)[(x+y)^2+(x+y)(x-y)+(x-y)^2]`
`=2y(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)`
`=2y(3x^2+y^2)`
a) \(\left(x+2\right)^2+2\left(x^2-4\right)+\left(x-2\right)^2\)
\(=\left(x+2\right)^2+2\left(x+2\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left(x+2+x-2\right)^2=\left(2x\right)^2=4x^2\)
b) \(x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2\)
c) \(\left(x+y\right)^3-\left(x-y\right)^3=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)=6x^2y+2y^3=2y\left(3x^2+y^2\right)\)
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\(a,2x\left(x-3\right)\\ b,x^2-\left(y+1\right)^2\\ =\left(x-y-1\right)\left(x+y+1\right)\)
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a:=2(x-2)+y(x-2)
=(x-2)(y+2)
b: \(=\left(x+y\right)^2-4\)
=(x+y+2)(x+y-2)
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\(a,=\left(x-2y\right)\left(x+2y\right)-2\left(x-2y\right)=\left(x-2y\right)\left(x+2y-2\right)\\ b,=\left(x^2+3y\right)^2-1=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)
\(a\left(x-y\right)+bx-by=a\left(x-y\right)+b\left(x-y\right)=\left(a+b\right)\left(x-y\right)\)
\(=a\left(x-y\right)+b\left(x-y\right)=\left(x-y\right)\left(a+b\right)\)