32³ + 19³ - 38³ + 312 is equal to:

The correct answer is -14933.

To evaluate the given expression step-by-step:

${32}^3+{19}^3-{38}^3+312$

Step 1: Calculate each individual cubic term.

First, calculate ${32}^3$:

${32}^2=1024$

${32}^3=1024\times 32=32768$

Next, calculate ${19}^3$:

${19}^2=361$

${19}^3=361\times 19=6859$

Then, calculate ${38}^3$:

${38}^2=1444$

${38}^3=1444\times 38=54872$

Step 2: Substitute the calculated values back into the expression.

$32768+6859-54872+312$

Step 3: Combine positive and negative numbers.

Sum of the positive terms:

$32768+6859+312=39939$

Subtract $54872$ from $39939$:

$39939-54872=-14933$

Thus, the value of the expression is -14933.