Answer:
[tex]101 * 102 = 10302[/tex]
Step-by-step explanation:
Given
[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]
Required
Find 101 * 102
[tex]101 * 102 =[/tex]
Express as a sum of 100
[tex](100 + 1) * (100 + 2)[/tex]
Compare this to [tex](x + a)(x + b)[/tex]
We have that:
[tex]x = 100[/tex]
[tex]a = 1[/tex]
[tex]b = 2[/tex]
Recall that:
[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]
Substitute 100 for x, 1 for a and 2 for b
[tex](100 + 1) * (100 + 2) = 100^2 + (1 + 2) * 100 + 1 * 2[/tex]
[tex](100 + 1) * (100 + 2) = 100^2 + 3 * 100 + 2[/tex]
[tex](100 + 1) * (100 + 2) = 10000 + 300 + 2[/tex]
[tex](100 + 1) * (100 + 2) = 10302[/tex]
Hence:
[tex]101 * 102 = 10302[/tex]
