Solve 25(x-y)^2+10(y-x)+1

$$25 ( x - y ) ^ { 2 } + 10 ( y - x ) + 1$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

Use the distributive property to multiply 25 by x^{2}-2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}+10\left(y-x\right)+1$$

Use the distributive property to multiply 10 by y-x.

$$25x^{2}-50xy+25y^{2}+10y-10x+1$$

Expand

$$25x^{2}-50xy-10x+25y^{2}+10y+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

Use the distributive property to multiply 25 by x^{2}-2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}+10\left(y-x\right)+1$$

Use the distributive property to multiply 10 by y-x.

$$25x^{2}-50xy+25y^{2}+10y-10x+1$$