Solve (k-4y/3)^2+y^2-8(k-4y^2/3)

$$( \frac { k - 4 y } { 3 } ) ^ { 2 } + y ^ { 2 } - 8 ( \frac { k - 4 y ^ { 2 } } { 3 } )$$

Evaluate

$$\frac{121y^{2}-8ky+k^{2}-24k}{9}$$

Short Solution Steps

To raise \frac{k-4y}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(k-4y\right)^{2}}{3^{2}}+y^{2}-8\times \frac{k-4y^{2}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{3^{2}}{3^{2}}.

$$\frac{\left(k-4y\right)^{2}}{3^{2}}+\frac{y^{2}\times 3^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

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

$$\frac{\left(k-4y\right)^{2}+y^{2}\times 3^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

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

$$\frac{k^{2}-8ky+16y^{2}+9y^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

Combine like terms in k^{2}-8ky+16y^{2}+9y^{2}.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

Express 8\times \frac{k-4y^{2}}{3} as a single fraction.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-\frac{8\left(k-4y^{2}\right)}{3}$$

Use the distributive property to multiply 8 by k-4y^{2}.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-\frac{8k-32y^{2}}{3}$$

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{8k-32y^{2}}{3} times \frac{3}{3}.

$$\frac{k^{2}+25y^{2}-8ky}{9}-\frac{3\left(8k-32y^{2}\right)}{9}$$

Since \frac{k^{2}+25y^{2}-8ky}{9} and \frac{3\left(8k-32y^{2}\right)}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{k^{2}+25y^{2}-8ky-3\left(8k-32y^{2}\right)}{9}$$

Do the multiplications in k^{2}+25y^{2}-8ky-3\left(8k-32y^{2}\right).

$$\frac{k^{2}+25y^{2}-8ky-24k+96y^{2}}{9}$$

Combine like terms in k^{2}+25y^{2}-8ky-24k+96y^{2}.

$$\frac{k^{2}-8ky+121y^{2}-24k}{9}$$

Expand

$$-\frac{8ky}{9}+\frac{121y^{2}}{9}+\frac{k^{2}}{9}-\frac{8k}{3}$$

Short Solution Steps

To raise \frac{k-4y}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(k-4y\right)^{2}}{3^{2}}+y^{2}-8\times \frac{k-4y^{2}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{3^{2}}{3^{2}}.

$$\frac{\left(k-4y\right)^{2}}{3^{2}}+\frac{y^{2}\times 3^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

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

$$\frac{\left(k-4y\right)^{2}+y^{2}\times 3^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

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

$$\frac{k^{2}-8ky+16y^{2}+9y^{2}}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

Combine like terms in k^{2}-8ky+16y^{2}+9y^{2}.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-8\times \frac{k-4y^{2}}{3}$$

Express 8\times \frac{k-4y^{2}}{3} as a single fraction.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-\frac{8\left(k-4y^{2}\right)}{3}$$

Use the distributive property to multiply 8 by k-4y^{2}.

$$\frac{k^{2}+25y^{2}-8ky}{3^{2}}-\frac{8k-32y^{2}}{3}$$

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{8k-32y^{2}}{3} times \frac{3}{3}.

$$\frac{k^{2}+25y^{2}-8ky}{9}-\frac{3\left(8k-32y^{2}\right)}{9}$$

Since \frac{k^{2}+25y^{2}-8ky}{9} and \frac{3\left(8k-32y^{2}\right)}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{k^{2}+25y^{2}-8ky-3\left(8k-32y^{2}\right)}{9}$$

Do the multiplications in k^{2}+25y^{2}-8ky-3\left(8k-32y^{2}\right).

$$\frac{k^{2}+25y^{2}-8ky-24k+96y^{2}}{9}$$

Combine like terms in k^{2}+25y^{2}-8ky-24k+96y^{2}.

$$\frac{k^{2}-8ky+121y^{2}-24k}{9}$$