Solve (p/2+4)(2p+6)

$$( \frac { p } { 2 } + 4 ) ( 2 p + 6 )$$

Evaluate

$$\left(p+3\right)\left(p+8\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\left(\frac{p}{2}+\frac{4\times 2}{2}\right)\left(2p+6\right)$$

Since \frac{p}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{p+4\times 2}{2}\left(2p+6\right)$$

Do the multiplications in p+4\times 2.

$$\frac{p+8}{2}\left(2p+6\right)$$

Express \frac{p+8}{2}\left(2p+6\right) as a single fraction.

$$\frac{\left(p+8\right)\left(2p+6\right)}{2}$$

Apply the distributive property by multiplying each term of p+8 by each term of 2p+6.

$$\frac{2p^{2}+6p+16p+48}{2}$$

Combine 6p and 16p to get 22p.

$$\frac{2p^{2}+22p+48}{2}$$

Divide each term of 2p^{2}+22p+48 by 2 to get 24+11p+p^{2}.

$$24+11p+p^{2}$$

Expand

$$p^{2}+11p+24$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\left(\frac{p}{2}+\frac{4\times 2}{2}\right)\left(2p+6\right)$$

Since \frac{p}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{p+4\times 2}{2}\left(2p+6\right)$$

Do the multiplications in p+4\times 2.

$$\frac{p+8}{2}\left(2p+6\right)$$

Express \frac{p+8}{2}\left(2p+6\right) as a single fraction.

$$\frac{\left(p+8\right)\left(2p+6\right)}{2}$$

Apply the distributive property by multiplying each term of p+8 by each term of 2p+6.

$$\frac{2p^{2}+6p+16p+48}{2}$$

Combine 6p and 16p to get 22p.

$$\frac{2p^{2}+22p+48}{2}$$

Divide each term of 2p^{2}+22p+48 by 2 to get 24+11p+p^{2}.

$$24+11p+p^{2}$$