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1.
A)x^4+x^3y-xy^3-y^4=
B) xy^2-6y^2-ax+ab+y^2-a=
C) x^2-5x+6=
2.
3x+3y
-7x+ax
14ab+21a
25xy^2-10x^2y
3.
x^3-5x^2+3x
2x^8+4x^7+6x^2
4.
3(x-2) -5x(x-2)
(5+m) (n-1) -(2m+3) (1-n)
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Answers & Comments
A)x^4+x^3y-xy^3-y^4=x³(x+y)-y³(x+y)=(x+y)(x³-y³)=(x+y)(x-y)(x²+xy+y²)
B) xy^2-by^2-ax+ab+y^2-a=y²(x-b+1)-a(x-b+1)=(y²-a)(x-b+1)
C) x^2-5x+6=(x²-2x)-(3x-6)=x(x-2)-3(x-2)=(x-2)(x-3)
2.
3x+3y=3(x+y)
-7x+ax=x(a-7)
14ab+21a=7a(2b+3)
25xy^2-10x^2y5xy(5y-2x)
3.
x^3-5x^2+3x=x(x²-5x+3)
2x^8+4x^7+6x^2=x²(2x^4+4x^5+6)
4.
3(x-2) -5x(x-2) =(x-2)(3-5x)
(5+m) (n-1) -(2m+3) (1-n)=(5+m) (n-1) +(2m+3) (n-1)=
=(n-1)(5+m+2m+3)=(n-1)(3m+8)