Solve 25(x+y)^2-36(x-2y)^2

$$25 ( x + y ) ^ { 2 } - 36 ( x - 2 y ) ^ { 2 }$$

Evaluate

$$\left(11x-7y\right)\left(17y-x\right)$$

Solution Steps

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

$$25\left(x^{2}+2xy+y^{2}\right)-36\left(x-2y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-36\left(x-2y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-36\left(x^{2}-4xy+4y^{2}\right)$$

Use the distributive property to multiply -36 by x^{2}-4xy+4y^{2}.

$$25x^{2}+50xy+25y^{2}-36x^{2}+144xy-144y^{2}$$

Combine 25x^{2} and -36x^{2} to get -11x^{2}.

$$-11x^{2}+50xy+25y^{2}+144xy-144y^{2}$$

Combine 50xy and 144xy to get 194xy.

$$-11x^{2}+194xy+25y^{2}-144y^{2}$$

Combine 25y^{2} and -144y^{2} to get -119y^{2}.

$$-11x^{2}+194xy-119y^{2}$$

Expand

$$-11x^{2}+194xy-119y^{2}$$

Solution Steps

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

$$25\left(x^{2}+2xy+y^{2}\right)-36\left(x-2y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-36\left(x-2y\right)^{2}$$

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

$$25x^{2}+50xy+25y^{2}-36\left(x^{2}-4xy+4y^{2}\right)$$

Use the distributive property to multiply -36 by x^{2}-4xy+4y^{2}.

$$25x^{2}+50xy+25y^{2}-36x^{2}+144xy-144y^{2}$$

Combine 25x^{2} and -36x^{2} to get -11x^{2}.

$$-11x^{2}+50xy+25y^{2}+144xy-144y^{2}$$

Combine 50xy and 144xy to get 194xy.

$$-11x^{2}+194xy+25y^{2}-144y^{2}$$

Combine 25y^{2} and -144y^{2} to get -119y^{2}.

$$-11x^{2}+194xy-119y^{2}$$