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

$$( 3 x + 2 y ) ( 3 x - 2 y ) - y ( x - 4 y ) =$$

Evaluate

$$x\left(9x-y\right)$$

Solution Steps

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

$$\left(3x\right)^{2}-\left(2y\right)^{2}-y\left(x-4y\right)$$

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

$$3^{2}x^{2}-\left(2y\right)^{2}-y\left(x-4y\right)$$

Calculate 3 to the power of 2 and get 9.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply y by x-4y.

$$9x^{2}-4y^{2}-\left(yx-4y^{2}\right)$$

To find the opposite of yx-4y^{2}, find the opposite of each term.

$$9x^{2}-4y^{2}-yx-\left(-4y^{2}\right)$$

The opposite of -4y^{2} is 4y^{2}.

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

Combine -4y^{2} and 4y^{2} to get 0.

$$9x^{2}-yx$$

Expand

$$9x^{2}-xy$$

Solution Steps

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

$$\left(3x\right)^{2}-\left(2y\right)^{2}-y\left(x-4y\right)$$

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

$$3^{2}x^{2}-\left(2y\right)^{2}-y\left(x-4y\right)$$

Calculate 3 to the power of 2 and get 9.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply y by x-4y.

$$9x^{2}-4y^{2}-\left(yx-4y^{2}\right)$$

To find the opposite of yx-4y^{2}, find the opposite of each term.

$$9x^{2}-4y^{2}-yx-\left(-4y^{2}\right)$$

The opposite of -4y^{2} is 4y^{2}.

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

Combine -4y^{2} and 4y^{2} to get 0.

$$9x^{2}-yx$$