Solve 9left(x+yright)^2-49left(x-yright)^2

$$9 { \left(x+y \right) }^{ 2 } -49 { \left(x-y \right) }^{ 2 }$$

Evaluate

$$4\left(5x-2y\right)\left(5y-2x\right)$$

Solution Steps

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

$$9\left(x^{2}+2xy+y^{2}\right)-49\left(x-y\right)^{2}$$

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

$$9x^{2}+18xy+9y^{2}-49\left(x-y\right)^{2}$$

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

$$9x^{2}+18xy+9y^{2}-49\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -49 by x^{2}-2xy+y^{2}.

$$9x^{2}+18xy+9y^{2}-49x^{2}+98xy-49y^{2}$$

Combine 9x^{2} and -49x^{2} to get -40x^{2}.

$$-40x^{2}+18xy+9y^{2}+98xy-49y^{2}$$

Combine 18xy and 98xy to get 116xy.

$$-40x^{2}+116xy+9y^{2}-49y^{2}$$

Combine 9y^{2} and -49y^{2} to get -40y^{2}.

$$-40x^{2}+116xy-40y^{2}$$

Expand

$$-40x^{2}+116xy-40y^{2}$$

Solution Steps

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

$$9\left(x^{2}+2xy+y^{2}\right)-49\left(x-y\right)^{2}$$

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

$$9x^{2}+18xy+9y^{2}-49\left(x-y\right)^{2}$$

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

$$9x^{2}+18xy+9y^{2}-49\left(x^{2}-2xy+y^{2}\right)$$

Use the distributive property to multiply -49 by x^{2}-2xy+y^{2}.

$$9x^{2}+18xy+9y^{2}-49x^{2}+98xy-49y^{2}$$

Combine 9x^{2} and -49x^{2} to get -40x^{2}.

$$-40x^{2}+18xy+9y^{2}+98xy-49y^{2}$$

Combine 18xy and 98xy to get 116xy.

$$-40x^{2}+116xy+9y^{2}-49y^{2}$$

Combine 9y^{2} and -49y^{2} to get -40y^{2}.

$$-40x^{2}+116xy-40y^{2}$$