Sure! Let's calculate [tex]\(4 \nabla 2\)[/tex] step-by-step using the given operation definition [tex]\( V \nabla W = (V^2 + W^2)(V - W) \)[/tex].
1. Substitute [tex]\(V = 4\)[/tex] and [tex]\(W = 2\)[/tex] into the formula:
[tex]\[
4 \nabla 2 = (4^2 + 2^2)(4 - 2)
\][/tex]
2. Calculate the squares of the numbers:
[tex]\[
4^2 = 16 \quad \text{and} \quad 2^2 = 4
\][/tex]
3. Add the squares:
[tex]\[
16 + 4 = 20
\][/tex]
4. Calculate the difference [tex]\(4 - 2\)[/tex]:
[tex]\[
4 - 2 = 2
\][/tex]
5. Multiply the sum of the squares by the difference:
[tex]\[
20 \times 2 = 40
\][/tex]
So, the result of [tex]\(4 \nabla 2\)[/tex] is:
[tex]\[
40
\][/tex]
