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

$$(3x-2y)(3x-2y)-(2x-3y)(2x-3y)$$

Evaluate

$$5\left(x^{2}-y^{2}\right)$$

Solution Steps

Multiply 3x-2y and 3x-2y to get \left(3x-2y\right)^{2}.

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

Multiply 2x-3y and 2x-3y to get \left(2x-3y\right)^{2}.

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

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

$$9x^{2}-12xy+4y^{2}-\left(2x-3y\right)^{2}$$

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

$$9x^{2}-12xy+4y^{2}-\left(4x^{2}-12xy+9y^{2}\right)$$

To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.

$$9x^{2}-12xy+4y^{2}-4x^{2}-\left(-12xy\right)-9y^{2}$$

The opposite of -12xy is 12xy.

$$9x^{2}-12xy+4y^{2}-4x^{2}+12xy-9y^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}-12xy+4y^{2}+12xy-9y^{2}$$

Combine -12xy and 12xy to get 0.

$$5x^{2}+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$5x^{2}-5y^{2}$$

Expand

$$5x^{2}-5y^{2}$$

Solution Steps

Multiply 3x-2y and 3x-2y to get \left(3x-2y\right)^{2}.

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

Multiply 2x-3y and 2x-3y to get \left(2x-3y\right)^{2}.

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

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

$$9x^{2}-12xy+4y^{2}-\left(2x-3y\right)^{2}$$

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

$$9x^{2}-12xy+4y^{2}-\left(4x^{2}-12xy+9y^{2}\right)$$

To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.

$$9x^{2}-12xy+4y^{2}-4x^{2}-\left(-12xy\right)-9y^{2}$$

The opposite of -12xy is 12xy.

$$9x^{2}-12xy+4y^{2}-4x^{2}+12xy-9y^{2}$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}-12xy+4y^{2}+12xy-9y^{2}$$

Combine -12xy and 12xy to get 0.

$$5x^{2}+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$5x^{2}-5y^{2}$$