Solve 36(x+y)^2-49(x-2y)^2

$$36 ( x + y ) ^ { 2 } - 49 ( x - 2 y ) ^ { 2 }$$

Evaluate

$$\left(13x-8y\right)\left(20y-x\right)$$

Solution Steps

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

$$36\left(x^{2}+2xy+y^{2}\right)-49\left(x-2y\right)^{2}$$

Use the distributive property to multiply 36 by x^{2}+2xy+y^{2}.

$$36x^{2}+72xy+36y^{2}-49\left(x-2y\right)^{2}$$

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

$$36x^{2}+72xy+36y^{2}-49\left(x^{2}-4xy+4y^{2}\right)$$

Use the distributive property to multiply -49 by x^{2}-4xy+4y^{2}.

$$36x^{2}+72xy+36y^{2}-49x^{2}+196xy-196y^{2}$$

Combine 36x^{2} and -49x^{2} to get -13x^{2}.

$$-13x^{2}+72xy+36y^{2}+196xy-196y^{2}$$

Combine 72xy and 196xy to get 268xy.

$$-13x^{2}+268xy+36y^{2}-196y^{2}$$

Combine 36y^{2} and -196y^{2} to get -160y^{2}.

$$-13x^{2}+268xy-160y^{2}$$

Expand

$$-13x^{2}+268xy-160y^{2}$$

Solution Steps

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

$$36\left(x^{2}+2xy+y^{2}\right)-49\left(x-2y\right)^{2}$$

Use the distributive property to multiply 36 by x^{2}+2xy+y^{2}.

$$36x^{2}+72xy+36y^{2}-49\left(x-2y\right)^{2}$$

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

$$36x^{2}+72xy+36y^{2}-49\left(x^{2}-4xy+4y^{2}\right)$$

Use the distributive property to multiply -49 by x^{2}-4xy+4y^{2}.

$$36x^{2}+72xy+36y^{2}-49x^{2}+196xy-196y^{2}$$

Combine 36x^{2} and -49x^{2} to get -13x^{2}.

$$-13x^{2}+72xy+36y^{2}+196xy-196y^{2}$$

Combine 72xy and 196xy to get 268xy.

$$-13x^{2}+268xy+36y^{2}-196y^{2}$$

Combine 36y^{2} and -196y^{2} to get -160y^{2}.

$$-13x^{2}+268xy-160y^{2}$$