Question

Evaluate 105*106 without multiplying directly

Answer 1

105 × 106
= (100+5) (100+6)
= 100(100)+100(6) + 5(100) + 5(6)
= 10000+600 + 500+30
= 10000+1100+30
= 11130

Hope it helps

Answer 2

105 × 106 = 11130

Given :

The expression 105 × 106

To find :

The product

Formula :

We are aware of the identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is 105 × 106

Step 2 of 2 :

Find the product

We are aware of identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

We take y = 100 , a = 5 , b = 6

Thus we get

$\displaystyle \sf{ 105 \times 106 }$

$\displaystyle \sf{ = (100 + 5 )\times (100 + 6 )}$

$\displaystyle \sf{ = {(100)}^{2} + (5 + 6) \times 100 + (5 \times 6)}$

$\displaystyle \sf{ = 10000 + (11 \times 100) + 30}$

$\displaystyle \sf{ = 10000 + 1100 + 30}$

$\displaystyle \sf{ = 11130}$

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