Solve left(3x-4yright)^2-left(3x+4yright)^2-xy

$${ \left(3x-4y \right) }^{ 2 } - { \left(3x+4y \right) }^{ 2 } -xy$$

Evaluate

$$-49xy$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-\left(3x+4y\right)^{2}-xy$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-\left(9x^{2}+24xy+16y^{2}\right)-xy$$

To find the opposite of 9x^{2}+24xy+16y^{2}, find the opposite of each term.

$$9x^{2}-24xy+16y^{2}-9x^{2}-24xy-16y^{2}-xy$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-24xy+16y^{2}-24xy-16y^{2}-xy$$

Combine -24xy and -24xy to get -48xy.

$$-48xy+16y^{2}-16y^{2}-xy$$

Combine 16y^{2} and -16y^{2} to get 0.

$$-48xy-xy$$

Combine -48xy and -xy to get -49xy.

$$-49xy$$

Expand

$$-49xy$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-\left(3x+4y\right)^{2}-xy$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4y\right)^{2}.

$$9x^{2}-24xy+16y^{2}-\left(9x^{2}+24xy+16y^{2}\right)-xy$$

To find the opposite of 9x^{2}+24xy+16y^{2}, find the opposite of each term.

$$9x^{2}-24xy+16y^{2}-9x^{2}-24xy-16y^{2}-xy$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-24xy+16y^{2}-24xy-16y^{2}-xy$$

Combine -24xy and -24xy to get -48xy.

$$-48xy+16y^{2}-16y^{2}-xy$$

Combine 16y^{2} and -16y^{2} to get 0.

$$-48xy-xy$$

Combine -48xy and -xy to get -49xy.

$$-49xy$$