Question

use identities to evaluate (101)²

Answer 1

${101}^{2} \\ = {(100 + 1)}^{2} \\ = {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ = {100}^{2} + 2 \times 100 \times 1 + {1}^{2} \\ = 10000 + 200 + 1 = 10201$

Answer 2

Answer: 10201

Step-by-step explanation:

We can evaluate this easily, without actually multiplying, by using the following identity.

(a + b)² = a² + b² + 2ab

We can write 101 = 100 + 1.

(101)²

= (100 + 1)²

= (100)² + (1)² + 2(100)(1)

= 10000 + 1 + 200

= 10201

More information:

Have you wondered why (a + b)² = a² + b² + 2ab? Read on if you don't know and want to know.

(a + b)²

= (a + b)(a + b)

=  a(a + b) + b(a + b)

= a² + ab + ab + b²

= a² + 2ab + b²