Solve [6^2-(6-2a)(6+2a)]

$$[ 6 ^ { 2 } - ( 6 - 2 a ) ( 6 + 2 a ) ]$$

Evaluate

$$4a^{2}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$36-\left(6-2a\right)\left(6+2a\right)$$

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

$$36-\left(6^{2}-\left(2a\right)^{2}\right)$$

Calculate 6 to the power of 2 and get 36.

$$36-\left(36-\left(2a\right)^{2}\right)$$

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

$$36-\left(36-2^{2}a^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$36-\left(36-4a^{2}\right)$$

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

$$36-36-\left(-4a^{2}\right)$$

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

$$36-36+4a^{2}$$

Subtract 36 from 36 to get 0.

$$4a^{2}$$

Expand

$$4a^{2}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$36-\left(6-2a\right)\left(6+2a\right)$$

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

$$36-\left(6^{2}-\left(2a\right)^{2}\right)$$

Calculate 6 to the power of 2 and get 36.

$$36-\left(36-\left(2a\right)^{2}\right)$$

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

$$36-\left(36-2^{2}a^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$36-\left(36-4a^{2}\right)$$

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

$$36-36-\left(-4a^{2}\right)$$

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

$$36-36+4a^{2}$$

Subtract 36 from 36 to get 0.

$$4a^{2}$$