Solve (x-3y)^2-2(9y^2-x^2)+(x+3y)^2

$$( x - 3 y ) ^ { 2 } - 2 ( 9 y ^ { 2 } - x ^ { 2 } ) + ( x + 3 y ) ^ { 2 }$$

Evaluate

$$4x^{2}$$

Solution Steps

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

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

Use the distributive property to multiply -2 by 9y^{2}-x^{2}.

$$x^{2}-6xy+9y^{2}-18y^{2}+2x^{2}+\left(x+3y\right)^{2}$$

Combine 9y^{2} and -18y^{2} to get -9y^{2}.

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

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

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

$$3x^{2}-6xy-9y^{2}+x^{2}+6xy+9y^{2}$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-6xy-9y^{2}+6xy+9y^{2}$$

Combine -6xy and 6xy to get 0.

$$4x^{2}-9y^{2}+9y^{2}$$

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

$$4x^{2}$$

Expand

$$4x^{2}$$

Solution Steps

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

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

Use the distributive property to multiply -2 by 9y^{2}-x^{2}.

$$x^{2}-6xy+9y^{2}-18y^{2}+2x^{2}+\left(x+3y\right)^{2}$$

Combine 9y^{2} and -18y^{2} to get -9y^{2}.

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

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

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

$$3x^{2}-6xy-9y^{2}+x^{2}+6xy+9y^{2}$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-6xy-9y^{2}+6xy+9y^{2}$$

Combine -6xy and 6xy to get 0.

$$4x^{2}-9y^{2}+9y^{2}$$

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

$$4x^{2}$$