Solve 8(x-y)^2-50(2x+y)^2

$$8 ( x - y ) ^ { 2 } - 50 ( 2 x + y ) ^ { 2 }$$

Evaluate

$$-6\left(4x+y\right)\left(8x+7y\right)$$

Solution Steps

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

$$8\left(x^{2}-2xy+y^{2}\right)-50\left(2x+y\right)^{2}$$

Use the distributive property to multiply 8 by x^{2}-2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-50\left(2x+y\right)^{2}$$

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

$$8x^{2}-16xy+8y^{2}-50\left(4x^{2}+4xy+y^{2}\right)$$

Use the distributive property to multiply -50 by 4x^{2}+4xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-200x^{2}-200xy-50y^{2}$$

Combine 8x^{2} and -200x^{2} to get -192x^{2}.

$$-192x^{2}-16xy+8y^{2}-200xy-50y^{2}$$

Combine -16xy and -200xy to get -216xy.

$$-192x^{2}-216xy+8y^{2}-50y^{2}$$

Combine 8y^{2} and -50y^{2} to get -42y^{2}.

$$-192x^{2}-216xy-42y^{2}$$

Expand

$$-192x^{2}-216xy-42y^{2}$$

Solution Steps

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

$$8\left(x^{2}-2xy+y^{2}\right)-50\left(2x+y\right)^{2}$$

Use the distributive property to multiply 8 by x^{2}-2xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-50\left(2x+y\right)^{2}$$

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

$$8x^{2}-16xy+8y^{2}-50\left(4x^{2}+4xy+y^{2}\right)$$

Use the distributive property to multiply -50 by 4x^{2}+4xy+y^{2}.

$$8x^{2}-16xy+8y^{2}-200x^{2}-200xy-50y^{2}$$

Combine 8x^{2} and -200x^{2} to get -192x^{2}.

$$-192x^{2}-16xy+8y^{2}-200xy-50y^{2}$$

Combine -16xy and -200xy to get -216xy.

$$-192x^{2}-216xy+8y^{2}-50y^{2}$$

Combine 8y^{2} and -50y^{2} to get -42y^{2}.

$$-192x^{2}-216xy-42y^{2}$$