a/ \(ab+bd-ac-cd\)
\(=\left(ab+ac\right)-\left(bd+cd\right)\)
\(=a\left(b+c\right)-d\left(b+c\right)\)
\(=\left(b+c\right)\left(a-d\right)\)
b/ \(ax+by-ay-bx\)
\(=\left(ax-ay\right)-\left(bx-by\right)\)
\(=a\left(x-y\right)-b\left(x-y\right)\)
\(=\left(x-y\right)\left(a-b\right)\)
c/ \(x^2-xy-xy+y^2\)
\(=\left(x^2-xy\right)-\left(xy-y^2\right)\)
\(=x\left(x-y\right)-y\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y\right)\)
a) \(ab+bd-ac-cd\)
\(=\left(ab+bd\right)-\left(ac+cd\right)\)
\(=b\left(a+d\right)-c\left(a+d\right)\)
\(=\left(a+d\right)\left(b-c\right)\)
b) \(ax+by-ay-bx\)
\(=ax-bx+by-ay\)
\(=\left(ax-bx\right)-\left(ay-by\right)\)
\(=x\left(a-b\right)-y\left(a-b\right)\)
\(=\left(a-b\right)\left(x-y\right)\)
c) \(x^2-xy-xy+y^2\)
\(=\left(x^2-xy\right)-\left(xy-y^2\right)\)
\(=x\left(x-y\right)-y\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y\right)\)
\(=\left(x-y\right)^2\)
Từ hằng kết quả trên ta suy ra được hằng đẳng thức :
\(x^2-2xy+y^2\) :)
