Solve 25left(x-yright)^2-9left(x+yright)^2

$$25 { \left(x-y \right) }^{ 2 } -9 { \left(x+y \right) }^{ 2 }$$

Evaluate

$$4\left(x-4y\right)\left(4x-y\right)$$

Solution Steps

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

$$25\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply -9 by x^{2}+2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 25x^{2} and -9x^{2} to get 16x^{2}.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

Combine -50xy and -18xy to get -68xy.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

Combine 25y^{2} and -9y^{2} to get 16y^{2}.

$$16x^{2}-68xy+16y^{2}$$

Expand

$$16x^{2}-68xy+16y^{2}$$

Solution Steps

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

$$25\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

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

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply -9 by x^{2}+2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 25x^{2} and -9x^{2} to get 16x^{2}.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

Combine -50xy and -18xy to get -68xy.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

Combine 25y^{2} and -9y^{2} to get 16y^{2}.

$$16x^{2}-68xy+16y^{2}$$