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\(ab\left(x^2+y^2\right)-xy\left(a^2+b^2\right)\)
\(=abx^2+aby^2-a^2xy-b^2xy\)
\(=ax\left(bx-ay\right)+by\left(ay-bx\right)\)
\(=ax\left(bx-ay\right)-by\left(bx-ay\right)\)
\(\left(bx-ay\right)\left(ax-by\right)\)
hãy k nếu bạn thấy đây là câu tl đúng :)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(xy+1\right)^2-\left(x-y\right)^2=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
\(=x^2y^2+xy-x^2y+xy^2+xy+1-x+y+x^2y+x-x^2+xy-xy^2-y+xy-y^2\)
\(=x^2y^2+2xy-x^2-y^2+1\)
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\(\left(x+y+z\right)\left(xy+yz+xz\right)-xyz=xy\left(x+y+z\right)-xyz+\left(yz+xz\right)\left(x+y+z\right)\)
\(=xy\left(x+y+z-z\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=xy\left(x+y\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]\)
\(=\left(x+y\right)\left(xy+xz+yz+z^2\right)\)
\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
Ta có
\(2x^2-xy-y^2=x^2-xy+x^2-y^2\) \(=x\left(x-y\right)+\left(x+y\right)\left(x-y\right)\)
\(=\left(x+x+y\right)\left(x-y\right)\)
\(=\left(2x+y\right)\left(x-y\right)\)