Question

find the square of 101 without doing actual multiplication

Answer 1

Answer:

$101^2=10201$

Step-by-step explanation:

Find the square of 101 without doing actual multiplication

I have used algebraic identity to find the square of 101.

Formula used:

$(a+b)^2=a^2+b^2+2ab$

Now,

$101^2$

$=(100+1)^2$

$=100^2+1^2+2*100*1$

$=10000+1+200$

$=10201$

$\implies\:101^2=10201$

Answer 2

$\huge\sf\pink{Answer}$

☞ (101)² = 10201

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➢ The square of 101 without actual multiplication

$\rule{110}1$

$\huge\sf\purple{Steps}$

(101)² can be written as (100+1)²

We us the identity,

✪ (a + b)² = a² + 2ab + b²

➳ (100 + 1)²

➳ (100)² + 2 * 1 * 100 + (1)²

➳ 10000 + 200 + 1

➳ 10201

$\rule{95}1$

$\sf\underline{\bullet{ More\; identities}}$

◕ (a-b)² = a² - 2ab + b²

◕ (a+b)(a-b) = a² - b²

◕ (a+b)³ = a³ + b³ + 3ab(a+b)

$\rule{170}3$