Solve 4-(2+u)(2-u)-u(u-6)

$$4 - ( 2 + u ) ( 2 - u ) - u ( u - 6 )$$

Evaluate

$$6u$$

Solution Steps

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

$$4-\left(2^{2}-u^{2}\right)-u\left(u-6\right)$$

Calculate 2 to the power of 2 and get 4.

$$4-\left(4-u^{2}\right)-u\left(u-6\right)$$

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

$$4-4-\left(-u^{2}\right)-u\left(u-6\right)$$

The opposite of -u^{2} is u^{2}.

$$4-4+u^{2}-u\left(u-6\right)$$

Subtract 4 from 4 to get 0.

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

Use the distributive property to multiply u by u-6.

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

To find the opposite of u^{2}-6u, find the opposite of each term.

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

The opposite of -6u is 6u.

$$u^{2}-u^{2}+6u$$

Combine u^{2} and -u^{2} to get 0.

$$6u$$

Expand

$$6u$$

Solution Steps

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

$$4-\left(2^{2}-u^{2}\right)-u\left(u-6\right)$$

Calculate 2 to the power of 2 and get 4.

$$4-\left(4-u^{2}\right)-u\left(u-6\right)$$

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

$$4-4-\left(-u^{2}\right)-u\left(u-6\right)$$

The opposite of -u^{2} is u^{2}.

$$4-4+u^{2}-u\left(u-6\right)$$

Subtract 4 from 4 to get 0.

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

Use the distributive property to multiply u by u-6.

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

To find the opposite of u^{2}-6u, find the opposite of each term.

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

The opposite of -6u is 6u.

$$u^{2}-u^{2}+6u$$

Combine u^{2} and -u^{2} to get 0.

$$6u$$