Answer :
To find the product of [tex]\(99 \times 99\)[/tex], we can use a mathematical technique for squaring numbers that are close to 100. Here's a step-by-step explanation:
1. Express 99 as a base of 100 minus a small number:
We can express 99 as [tex]\(100 - 1\)[/tex].
2. Use the formula for the square of a binomial:
[tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex].
In this case, [tex]\(a = 100\)[/tex] and [tex]\(b = 1\)[/tex].
3. Substitute into the formula:
[tex]\[
(100 - 1)^2 = 100^2 - 2 \times 100 \times 1 + 1^2
\][/tex]
4. Calculate each term:
- [tex]\(100^2 = 10000\)[/tex]
- [tex]\(2 \times 100 \times 1 = 200\)[/tex]
- [tex]\(1^2 = 1\)[/tex]
5. Combine the results:
[tex]\[
10000 - 200 + 1 = 9801
\][/tex]
Therefore, the product of [tex]\(99 \times 99\)[/tex] is [tex]\(9801\)[/tex].
1. Express 99 as a base of 100 minus a small number:
We can express 99 as [tex]\(100 - 1\)[/tex].
2. Use the formula for the square of a binomial:
[tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex].
In this case, [tex]\(a = 100\)[/tex] and [tex]\(b = 1\)[/tex].
3. Substitute into the formula:
[tex]\[
(100 - 1)^2 = 100^2 - 2 \times 100 \times 1 + 1^2
\][/tex]
4. Calculate each term:
- [tex]\(100^2 = 10000\)[/tex]
- [tex]\(2 \times 100 \times 1 = 200\)[/tex]
- [tex]\(1^2 = 1\)[/tex]
5. Combine the results:
[tex]\[
10000 - 200 + 1 = 9801
\][/tex]
Therefore, the product of [tex]\(99 \times 99\)[/tex] is [tex]\(9801\)[/tex].
