Solve 2left(x-yright)^2-9left(x-yright)+10

$$2 { \left(x-y \right) }^{ 2 } -9 \left( x-y \right) +10$$

Evaluate

$$\left(x-y-2\right)\left(2x-2y-5\right)$$

Solution Steps

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

$$2\left(x^{2}-2xy+y^{2}\right)-9\left(x-y\right)+10$$

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

$$2x^{2}-4xy+2y^{2}-9\left(x-y\right)+10$$

Use the distributive property to multiply -9 by x-y.

$$2x^{2}-4xy+2y^{2}-9x+9y+10$$

Expand

$$2x^{2}-4xy-9x+2y^{2}+9y+10$$

Solution Steps

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

$$2\left(x^{2}-2xy+y^{2}\right)-9\left(x-y\right)+10$$

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

$$2x^{2}-4xy+2y^{2}-9\left(x-y\right)+10$$

Use the distributive property to multiply -9 by x-y.

$$2x^{2}-4xy+2y^{2}-9x+9y+10$$