Answer :
Certainly! Let's solve the expression [tex]\(99^3 + 3(99^2) + 3(99) + 1\)[/tex] step-by-step.
This expression can be viewed as the expansion of a binomial expression [tex]\((a + 1)^3\)[/tex], where [tex]\(a = 99\)[/tex]. Let's break it down into its components:
1. Calculate [tex]\(99^3\)[/tex]:
[tex]\[
99^3 = 99 \times 99 \times 99 = 970,299
\][/tex]
2. Calculate [tex]\(3 \times 99^2\)[/tex]:
[tex]\[
99^2 = 99 \times 99 = 9,801
\][/tex]
[tex]\[
3 \times 99^2 = 3 \times 9,801 = 29,403
\][/tex]
3. Calculate [tex]\(3 \times 99\)[/tex]:
[tex]\[
3 \times 99 = 297
\][/tex]
4. Include the constant term:
[tex]\[
+1 = 1
\][/tex]
5. Add all the components together:
[tex]\[
970,299 + 29,403 + 297 + 1 = 1,000,000
\][/tex]
So the value of the expression [tex]\(99^3 + 3(99^2) + 3(99) + 1\)[/tex] is 1,000,000.
This expression can be viewed as the expansion of a binomial expression [tex]\((a + 1)^3\)[/tex], where [tex]\(a = 99\)[/tex]. Let's break it down into its components:
1. Calculate [tex]\(99^3\)[/tex]:
[tex]\[
99^3 = 99 \times 99 \times 99 = 970,299
\][/tex]
2. Calculate [tex]\(3 \times 99^2\)[/tex]:
[tex]\[
99^2 = 99 \times 99 = 9,801
\][/tex]
[tex]\[
3 \times 99^2 = 3 \times 9,801 = 29,403
\][/tex]
3. Calculate [tex]\(3 \times 99\)[/tex]:
[tex]\[
3 \times 99 = 297
\][/tex]
4. Include the constant term:
[tex]\[
+1 = 1
\][/tex]
5. Add all the components together:
[tex]\[
970,299 + 29,403 + 297 + 1 = 1,000,000
\][/tex]
So the value of the expression [tex]\(99^3 + 3(99^2) + 3(99) + 1\)[/tex] is 1,000,000.
