Question

1. Phân tích thành x tử
a, xy+1-x-y
b, ax+ay-3x-3y
c,x^3-2x²+2x-4
d,x²+ab+ax+bx
e,16-x²+2xy-y²
f,ax²+ax-bx²-bx-a+b

Answer 1

Answer 2

a) \(xy+1-x-y\)

\(=x\left(y-1\right)-\left(y-1\right)\)

\(=\left(y-1\right)\left(x-1\right)\)

b) \(ax+ay-3x-3y\)

\(=a\left(x+y\right)-3\left(x+y\right)\)

\(=\left(x+y\right)\left(a-3\right)\)

c) \(x^3-2x^2+2x-4\)

\(=x^2\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+2\right)\)

d) \(x^2+ab+ax+bx\)

\(=x\left(b+x\right)+a\left(b+x\right)\)

\(=\left(b+x\right)\left(a+x\right)\)

e) \(16-x^2+2xy-y^2\)

\(=16-\left(x^2-2xy+y^2\right)\)

\(=4^2-\left(x-y\right)^2\)

\(=\left(4-x+y\right)\left(4+x-y\right)\)

f) \(ax^2+ax-bx^2-bx-a+b\)

\(=\left(ax^2+ax-a\right)-\left(bx^2+bx-b\right)\)

\(=a\left(x^2+x-1\right)-b\left(x^2+x-1\right)\)

\(=\left(x^2+x-1\right)\left(a-b\right)\)

Answer 3

a) \(xy+1-x-y=\left(xy-x\right)+\left(1-y\right)=x\left(y-1\right)+\left(1-y\right)=x\left(y-1\right)-\left(y-1\right)=\left(x-1\right)\left(y-1\right)\)

b) \(ax+ay-3x-3y=a\left(x+y\right)-3\left(x-y\right)=\left(a-3\right)\left(x+y\right)\)

c) \(x^3-2x^2+2x-4=x^2\left(x-2\right)+2\left(x-2\right)=\left(x^2+2\right)\left(x-2\right)\)

d) \(x^2+ab+ax+bx=\left(x^2+ax\right)+\left(ab+bx\right)=x\left(x+a\right)+b\left(a+x\right)=\left(x+b\right)\left(x+a\right)\)

e) \(16-x^2+2xy-y^2=16-\left(x-y\right)^2=\left(4-x+y\right)\left(4+x-y\right)\)

f) \(ax^2+ax-bx^2-bx-a+b=\left(a-b\right)x^2+\left(a-b\right)x-a+b=\left(a-b\right)\left(x^2+x-1\right)\)