Question

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

Answer 1

Answer:

$101 * 102 = 10302$

Step-by-step 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:

$101 * 102 = 10302$