Question

plzzz solve full explanation

Answer 1

Here,

We need to find the value of 103 × 107 without actual multiplication.

Identity used:

• (x + a)(x + b) = x² + x(a + b) + ab

Now, we can split 103 into (100 + 3) and 107 into (100 + 7)

103 × 107

→ (100 + 3)(100 + 7)

Using the above identity and substituting the values,

• x = 100

• a = 3

• b = 7

103 × 107

= (100 + 3)(100 + 7)

= 100² + 100(3 + 7) + [3 × 7]

= 10000 + 100(10) + 21

= 10000 + 1000 + 21

= 11021

∴ 103 × 107 = 11021

Other useful identities:

1. (a + b)² = a² + b² + 2ab
2. (a - b)² = a² + b² - 2ab