Solve (3x-3y)^2-(-3x-4y)(-3x+4y)=

$$( 3 x - 3 y ) ^ { 2 } - ( - 3 x - 4 y ) ( - 3 x + 4 y ) =$$

Evaluate

$$y\left(25y-18x\right)$$

Solution Steps

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

$$9x^{2}-18xy+9y^{2}-\left(-3x-4y\right)\left(-3x+4y\right)$$

Consider \left(-3x-4y\right)\left(-3x+4y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$9x^{2}-18xy+9y^{2}-\left(\left(-3x\right)^{2}-\left(4y\right)^{2}\right)$$

Expand \left(-3x\right)^{2}.

$$9x^{2}-18xy+9y^{2}-\left(\left(-3\right)^{2}x^{2}-\left(4y\right)^{2}\right)$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-\left(4y\right)^{2}\right)$$

Expand \left(4y\right)^{2}.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-4^{2}y^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-16y^{2}\right)$$

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

$$9x^{2}-18xy+9y^{2}-9x^{2}+16y^{2}$$

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

$$-18xy+9y^{2}+16y^{2}$$

Combine 9y^{2} and 16y^{2} to get 25y^{2}.

$$-18xy+25y^{2}$$

Expand

$$25y^{2}-18xy$$

Solution Steps

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

$$9x^{2}-18xy+9y^{2}-\left(-3x-4y\right)\left(-3x+4y\right)$$

Consider \left(-3x-4y\right)\left(-3x+4y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$9x^{2}-18xy+9y^{2}-\left(\left(-3x\right)^{2}-\left(4y\right)^{2}\right)$$

Expand \left(-3x\right)^{2}.

$$9x^{2}-18xy+9y^{2}-\left(\left(-3\right)^{2}x^{2}-\left(4y\right)^{2}\right)$$

Calculate -3 to the power of 2 and get 9.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-\left(4y\right)^{2}\right)$$

Expand \left(4y\right)^{2}.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-4^{2}y^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$9x^{2}-18xy+9y^{2}-\left(9x^{2}-16y^{2}\right)$$

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

$$9x^{2}-18xy+9y^{2}-9x^{2}+16y^{2}$$

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

$$-18xy+9y^{2}+16y^{2}$$

Combine 9y^{2} and 16y^{2} to get 25y^{2}.

$$-18xy+25y^{2}$$