Select the correct answer.

What is the value of this expression if [tex][tex]$a=-7$[/tex][/tex] and [tex][tex]$b=-3$[/tex][/tex]?

[tex]\[ a^3 - b^2 \][/tex]

A. [tex]\quad-30[/tex]

B. -12

C. -334

D. -352



Answer :

To solve the given mathematical expression [tex]\(a^3 - b^2\)[/tex] for the values [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex], follow these steps:

1. Calculate [tex]\(a^3\)[/tex]:
- Given [tex]\(a = -7\)[/tex], we need to find [tex]\((-7)^3\)[/tex].
- When we cube [tex]\(-7\)[/tex], we get:
[tex]\[ (-7) \times (-7) \times (-7) = -343 \][/tex]

2. Calculate [tex]\(b^2\)[/tex]:
- Given [tex]\(b = -3\)[/tex], we need to find [tex]\((-3)^2\)[/tex].
- When we square [tex]\(-3\)[/tex], we get:
[tex]\[ (-3) \times (-3) = 9 \][/tex]

3. Subtract [tex]\(b^2\)[/tex] from [tex]\(a^3\)[/tex]:
- Now, we need to compute [tex]\(a^3 - b^2\)[/tex]:
[tex]\[ -343 - 9 = -352 \][/tex]

Thus, the value of the expression [tex]\(a^3 - b^2\)[/tex] when [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex] is [tex]\(-352\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{-352} \][/tex]