Solve left(6x+2right)^2-(6x+2)(6x-2)

$${ \left(6x+2 \right) }^{ 2 } -(6x+2)(6x-2)$$

Evaluate

$$24x+8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+2\right)^{2}.

$$36x^{2}+24x+4-\left(6x+2\right)\left(6x-2\right)$$

Consider \left(6x+2\right)\left(6x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$36x^{2}+24x+4-\left(\left(6x\right)^{2}-4\right)$$

Expand \left(6x\right)^{2}.

$$36x^{2}+24x+4-\left(6^{2}x^{2}-4\right)$$

Calculate 6 to the power of 2 and get 36.

$$36x^{2}+24x+4-\left(36x^{2}-4\right)$$

To find the opposite of 36x^{2}-4, find the opposite of each term.

$$36x^{2}+24x+4-36x^{2}+4$$

Combine 36x^{2} and -36x^{2} to get 0.

$$24x+4+4$$

Add 4 and 4 to get 8.

$$24x+8$$

Expand

$$24x+8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+2\right)^{2}.

$$36x^{2}+24x+4-\left(6x+2\right)\left(6x-2\right)$$

Consider \left(6x+2\right)\left(6x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$36x^{2}+24x+4-\left(\left(6x\right)^{2}-4\right)$$

Expand \left(6x\right)^{2}.

$$36x^{2}+24x+4-\left(6^{2}x^{2}-4\right)$$

Calculate 6 to the power of 2 and get 36.

$$36x^{2}+24x+4-\left(36x^{2}-4\right)$$

To find the opposite of 36x^{2}-4, find the opposite of each term.

$$36x^{2}+24x+4-36x^{2}+4$$

Combine 36x^{2} and -36x^{2} to get 0.

$$24x+4+4$$

Add 4 and 4 to get 8.

$$24x+8$$