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

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

Evaluate

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

Solution Steps

Consider \left(x+2y\right)\left(x-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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply 3x by x+3y.

$$x^{2}-4y^{2}+3x^{2}+9xy$$

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

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

Expand

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

Solution Steps

Consider \left(x+2y\right)\left(x-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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply 3x by x+3y.

$$x^{2}-4y^{2}+3x^{2}+9xy$$

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

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