Question

Use (x+a)(x+b)=x2+(a+b)x+ab find 101*102​

Answer 1

`101 * 102 = 10302`

Explanation:

Given

`(x + a)(x + b) = x^2 + (a + b)x + ab`

Required

Find 101 * 102

`101 * 102 =`

Express as a sum of 100

`(100 + 1) * (100 + 2)`

Compare this to
`(x + a)(x + b)`

We have that:

`x = 100`

`a = 1`

`b = 2`

Recall that:

`(x + a)(x + b) = x^2 + (a + b)x + ab`

Substitute 100 for x, 1 for a and 2 for b

`(100 + 1) * (100 + 2) = 100^2 + (1 + 2) * 100 + 1 * 2`

`(100 + 1) * (100 + 2) = 100^2 + 3 * 100 + 2`

`(100 + 1) * (100 + 2) = 10000 + 300 + 2`

`(100 + 1) * (100 + 2) = 10302`

Hence:

`101 * 102 = 10302`