Solve (6+k/3)^2+4*4-5k/3

$$( \frac { 6 + k } { 3 } ) ^ { 2 } + 4 \times \frac { 4 - 5 k } { 3 }$$

Evaluate

$$\frac{k^{2}}{9}-\frac{16k}{3}+\frac{28}{3}$$

Short Solution Steps

To raise \frac{6+k}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6+k\right)^{2}}{3^{2}}+4\times \frac{4-5k}{3}$$

Express 4\times \frac{4-5k}{3} as a single fraction.

$$\frac{\left(6+k\right)^{2}}{3^{2}}+\frac{4\left(4-5k\right)}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3^{2} and 3 is 9. Multiply \frac{4\left(4-5k\right)}{3} times \frac{3}{3}.

$$\frac{\left(6+k\right)^{2}}{9}+\frac{3\times 4\left(4-5k\right)}{9}$$

Since \frac{\left(6+k\right)^{2}}{9} and \frac{3\times 4\left(4-5k\right)}{9} have the same denominator, add them by adding their numerators.

$$\frac{\left(6+k\right)^{2}+3\times 4\left(4-5k\right)}{9}$$

Do the multiplications in \left(6+k\right)^{2}+3\times 4\left(4-5k\right).

$$\frac{36+12k+k^{2}+48-60k}{9}$$

Combine like terms in 36+12k+k^{2}+48-60k.

$$\frac{84-48k+k^{2}}{9}$$

Expand

$$\frac{k^{2}}{9}-\frac{16k}{3}+\frac{28}{3}$$

Short Solution Steps

To raise \frac{6+k}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6+k\right)^{2}}{3^{2}}+4\times \frac{4-5k}{3}$$

Express 4\times \frac{4-5k}{3} as a single fraction.

$$\frac{\left(6+k\right)^{2}}{3^{2}}+\frac{4\left(4-5k\right)}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3^{2} and 3 is 9. Multiply \frac{4\left(4-5k\right)}{3} times \frac{3}{3}.

$$\frac{\left(6+k\right)^{2}}{9}+\frac{3\times 4\left(4-5k\right)}{9}$$

Since \frac{\left(6+k\right)^{2}}{9} and \frac{3\times 4\left(4-5k\right)}{9} have the same denominator, add them by adding their numerators.

$$\frac{\left(6+k\right)^{2}+3\times 4\left(4-5k\right)}{9}$$

Do the multiplications in \left(6+k\right)^{2}+3\times 4\left(4-5k\right).

$$\frac{36+12k+k^{2}+48-60k}{9}$$

Combine like terms in 36+12k+k^{2}+48-60k.

$$\frac{84-48k+k^{2}}{9}$$