Solve -(3k-2)^2+(3k-1)^2/2+(3k)^2

$$- \frac { ( 3 k - 2 ) ^ { 2 } + ( 3 k - 1 ) ^ { 2 } } { 2 } + ( 3 k ) ^ { 2 }$$

Evaluate

$$9k-\frac{5}{2}$$

Short Solution Steps

Expand \left(3k\right)^{2}.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+3^{2}k^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+9k^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9k^{2} times \frac{2}{2}.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+\frac{2\times 9k^{2}}{2}$$

Since -\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2} and \frac{2\times 9k^{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\left(\left(3k-2\right)^{2}+\left(3k-1\right)^{2}\right)+2\times 9k^{2}}{2}$$

Do the multiplications in -\left(\left(3k-2\right)^{2}+\left(3k-1\right)^{2}\right)+2\times 9k^{2}.

$$\frac{-9k^{2}+12k-4-9k^{2}+6k-1+18k^{2}}{2}$$

Combine like terms in -9k^{2}+12k-4-9k^{2}+6k-1+18k^{2}.

$$\frac{18k-5}{2}$$

Expand

$$9k-\frac{5}{2}$$

Short Solution Steps

Expand \left(3k\right)^{2}.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+3^{2}k^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+9k^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9k^{2} times \frac{2}{2}.

$$-\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2}+\frac{2\times 9k^{2}}{2}$$

Since -\frac{\left(3k-2\right)^{2}+\left(3k-1\right)^{2}}{2} and \frac{2\times 9k^{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\left(\left(3k-2\right)^{2}+\left(3k-1\right)^{2}\right)+2\times 9k^{2}}{2}$$

Do the multiplications in -\left(\left(3k-2\right)^{2}+\left(3k-1\right)^{2}\right)+2\times 9k^{2}.

$$\frac{-9k^{2}+12k-4-9k^{2}+6k-1+18k^{2}}{2}$$

Combine like terms in -9k^{2}+12k-4-9k^{2}+6k-1+18k^{2}.

$$\frac{18k-5}{2}$$