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

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

Evaluate

$$6y\left(2x+3y\right)$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$12xy+9y^{2}+9y^{2}$$

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

$$12xy+18y^{2}$$

Expand

$$12xy+18y^{2}$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$12xy+9y^{2}+9y^{2}$$

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

$$12xy+18y^{2}$$