Answer :
To simplify the product [tex]\(101 \times 99\)[/tex], we can use the difference of squares formula. This formula states that:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
Let's consider:
- [tex]\(a = 100\)[/tex]
- [tex]\(b = 1\)[/tex]
This means [tex]\(101\)[/tex] becomes [tex]\((100 + 1)\)[/tex] and [tex]\(99\)[/tex] becomes [tex]\((100 - 1)\)[/tex].
Applying the difference of squares formula:
[tex]\[
(101 \times 99) = (100 + 1)(100 - 1)
\][/tex]
Using the formula, you get:
[tex]\[
= 100^2 - 1^2
\][/tex]
Now, calculate each square:
- [tex]\(100^2 = 10000\)[/tex]
- [tex]\(1^2 = 1\)[/tex]
Subtract these results:
[tex]\[
10000 - 1 = 9999
\][/tex]
Therefore, [tex]\(101 \times 99\)[/tex] simplifies to [tex]\(9999\)[/tex].
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
Let's consider:
- [tex]\(a = 100\)[/tex]
- [tex]\(b = 1\)[/tex]
This means [tex]\(101\)[/tex] becomes [tex]\((100 + 1)\)[/tex] and [tex]\(99\)[/tex] becomes [tex]\((100 - 1)\)[/tex].
Applying the difference of squares formula:
[tex]\[
(101 \times 99) = (100 + 1)(100 - 1)
\][/tex]
Using the formula, you get:
[tex]\[
= 100^2 - 1^2
\][/tex]
Now, calculate each square:
- [tex]\(100^2 = 10000\)[/tex]
- [tex]\(1^2 = 1\)[/tex]
Subtract these results:
[tex]\[
10000 - 1 = 9999
\][/tex]
Therefore, [tex]\(101 \times 99\)[/tex] simplifies to [tex]\(9999\)[/tex].
