Solve x^2+10xy-5x^2y-25xy^2+25y^2=

$$x ^ { 2 } + 10 x y - 5 x ^ { 2 } y - 25 x y ^ { 2 } + 25 y ^ { 2 } =$$

Factor

$$\left(x+5y\right)\left(5y+x-5xy\right)$$

Solution Steps

Consider x^{2}+10xy-5x^{2}y-25xy^{2}+25y^{2} as a polynomial over variable x.

$$\left(1-5y\right)x^{2}+\left(10y-25y^{2}\right)x+25y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power \left(1-5y\right)x^{2} and n divides the constant factor 25y^{2}. One such factor is x+5y. Factor the polynomial by dividing it by this factor.

$$\left(x+5y\right)\left(-5xy+x+5y\right)$$

Evaluate

$$\left(x+5y\right)\left(5y+x-5xy\right)$$