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

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

Evaluate

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

Solution Steps

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

$$9x^{2}-6xy+y^{2}-\left(x-3y\right)^{2}$$

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

$$9x^{2}-6xy+y^{2}-\left(x^{2}-6xy+9y^{2}\right)$$

To find the opposite of x^{2}-6xy+9y^{2}, find the opposite of each term.

$$9x^{2}-6xy+y^{2}-x^{2}+6xy-9y^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}-6xy+y^{2}+6xy-9y^{2}$$

Combine -6xy and 6xy to get 0.

$$8x^{2}+y^{2}-9y^{2}$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$8x^{2}-8y^{2}$$

Expand

$$8x^{2}-8y^{2}$$

Solution Steps

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

$$9x^{2}-6xy+y^{2}-\left(x-3y\right)^{2}$$

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

$$9x^{2}-6xy+y^{2}-\left(x^{2}-6xy+9y^{2}\right)$$

To find the opposite of x^{2}-6xy+9y^{2}, find the opposite of each term.

$$9x^{2}-6xy+y^{2}-x^{2}+6xy-9y^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}-6xy+y^{2}+6xy-9y^{2}$$

Combine -6xy and 6xy to get 0.

$$8x^{2}+y^{2}-9y^{2}$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$8x^{2}-8y^{2}$$