Solve a^22(2-a)(1/2+1/a)

$$a ^ { 2 } 2 ( 2 - a ) ( \frac { 1 } { 2 } + \frac { 1 } { a } )$$

Evaluate

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and a is 2a. Multiply \frac{1}{2} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{2}{2}.

$$a^{2}\times 2\left(2-a\right)\left(\frac{a}{2a}+\frac{2}{2a}\right)$$

Since \frac{a}{2a} and \frac{2}{2a} have the same denominator, add them by adding their numerators.

$$a^{2}\times 2\left(2-a\right)\times \frac{a+2}{2a}$$

Express a^{2}\times \frac{a+2}{2a} as a single fraction.

$$\frac{a^{2}\left(a+2\right)}{2a}\times 2\left(2-a\right)$$

Cancel out a in both numerator and denominator.

$$\frac{a\left(a+2\right)}{2}\times 2\left(2-a\right)$$

Use the distributive property to multiply a by a+2.

$$\frac{a^{2}+2a}{2}\times 2\left(2-a\right)$$

Cancel out 2 and 2.

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

Use the distributive property to multiply a^{2}+2a by 2-a and combine like terms.

$$-a^{3}+4a$$

Expand

$$4a-a^{3}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and a is 2a. Multiply \frac{1}{2} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{2}{2}.

$$a^{2}\times 2\left(2-a\right)\left(\frac{a}{2a}+\frac{2}{2a}\right)$$

Since \frac{a}{2a} and \frac{2}{2a} have the same denominator, add them by adding their numerators.

$$a^{2}\times 2\left(2-a\right)\times \frac{a+2}{2a}$$

Express a^{2}\times \frac{a+2}{2a} as a single fraction.

$$\frac{a^{2}\left(a+2\right)}{2a}\times 2\left(2-a\right)$$

Cancel out a in both numerator and denominator.

$$\frac{a\left(a+2\right)}{2}\times 2\left(2-a\right)$$

Use the distributive property to multiply a by a+2.

$$\frac{a^{2}+2a}{2}\times 2\left(2-a\right)$$

Cancel out 2 and 2.

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

Use the distributive property to multiply a^{2}+2a by 2-a and combine like terms.

$$-a^{3}+4a$$