Select the correct answer.

What is the value of this expression when [tex]c = -4[/tex] and [tex]d = 10[/tex]?

[tex]
\frac{1}{4}\left(c^3 + d^2\right)
[/tex]

A. 2
B. 9
C. 21
D. 41



Answer :

Sure, let's solve the expression step-by-step given [tex]\( c = -4 \)[/tex] and [tex]\( d = 10 \)[/tex].

We need to evaluate:
[tex]\[ \frac{1}{4}\left(c^3+d^2\right) \][/tex]

1. Calculate [tex]\(c^3\)[/tex]:
[tex]\[ c^3 = (-4)^3 = -4 \times -4 \times -4 = -64 \][/tex]

2. Calculate [tex]\(d^2\)[/tex]:
[tex]\[ d^2 = 10^2 = 10 \times 10 = 100 \][/tex]

3. Add the results of [tex]\(c^3\)[/tex] and [tex]\(d^2\)[/tex]:
[tex]\[ c^3 + d^2 = -64 + 100 = 36 \][/tex]

4. Multiply the sum by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{4} \times 36 = 9 \][/tex]

Therefore, the value of the expression is [tex]\( 9 \)[/tex].

The correct answer is:
[tex]\[ \boxed{9} \][/tex]