a) \(x^2+\left(a+b\right)xy+aby^2\)
\(=x^2+axy+bxy+aby^2\)
\(=x\left(x+ay\right)+by\left(x+ay\right)\)
\(=\left(x+ay\right)\left(x+by\right)\)
b) \(a^2-\left(c+d\right)ab+cdb^2\)
\(=a^2-abc-abd+cdb^2\)
\(=a\left(a-bc\right)-bd\left(a-bc\right)\)
\(=\left(a-bc\right)\left(a-bd\right)\)
c) Sửa đề: \(ab\left(x^2+y^2\right)+xy\left(a^2+b^2\right)\)
\(=abx^2+aby^2+a^2xy+b^2xy\)
\(=abx^2+b^2xy+a^2xy+aby^2\)
\(=bx\left(ax+by\right)+ay\left(ax+by\right)\)
\(=\left(ax+by\right)\left(bx+ay\right)\)
d) Sửa đề: \(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)
\(=x^2y^2+2abxy+a^2b^2+a^2y^2-2abxy+b^2x^2\)
\(=x^2y^2+a^2y^2+a^2b^2+b^2x^2\)
\(=y^2\left(x^2+a^2\right)+b^2\left(x^2+a^2\right)\)
\(=\left(x^2+a^2\right)\left(y^2+b^2\right)\)
