Solve (6x-7y)^2-(3x-3y)^2

$$( 6 x - 7 y ) ^ { 2 } - ( 3 x - 3 y ) ^ { 2 }$$

Evaluate

$$\left(3x-4y\right)\left(9x-10y\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-7y\right)^{2}.

$$36x^{2}-84xy+49y^{2}-\left(3x-3y\right)^{2}$$

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

$$36x^{2}-84xy+49y^{2}-\left(9x^{2}-18xy+9y^{2}\right)$$

To find the opposite of 9x^{2}-18xy+9y^{2}, find the opposite of each term.

$$36x^{2}-84xy+49y^{2}-9x^{2}+18xy-9y^{2}$$

Combine 36x^{2} and -9x^{2} to get 27x^{2}.

$$27x^{2}-84xy+49y^{2}+18xy-9y^{2}$$

Combine -84xy and 18xy to get -66xy.

$$27x^{2}-66xy+49y^{2}-9y^{2}$$

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

$$27x^{2}-66xy+40y^{2}$$

Expand

$$27x^{2}-66xy+40y^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-7y\right)^{2}.

$$36x^{2}-84xy+49y^{2}-\left(3x-3y\right)^{2}$$

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

$$36x^{2}-84xy+49y^{2}-\left(9x^{2}-18xy+9y^{2}\right)$$

To find the opposite of 9x^{2}-18xy+9y^{2}, find the opposite of each term.

$$36x^{2}-84xy+49y^{2}-9x^{2}+18xy-9y^{2}$$

Combine 36x^{2} and -9x^{2} to get 27x^{2}.

$$27x^{2}-84xy+49y^{2}+18xy-9y^{2}$$

Combine -84xy and 18xy to get -66xy.

$$27x^{2}-66xy+49y^{2}-9y^{2}$$

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

$$27x^{2}-66xy+40y^{2}$$