Question

evaluate 105 X 108 without multiply directory​

Answer 1

(105 × 108) can be written as (100 + 5) (100 + 8) . If we carefully observe ; it is in the form of (x + a) (x + b) where x = 100 and a = 5 and b = 8.

Following the same identity ; we will solve the given problem :

(x+a)(x+b) = x² + (a+b)x + ab

Substituting the values :

➜(x+a)(x+b) = (100)² + (5 + 8)100 + 5×8

Simplification :

➜(x+a)(x+b) = 10000 + (13)100 + 40

➜(x+a)(x+b) = 10000 + 1300 + 40

➜(x+a)(x+b) = 11340

Verification :

➜ 105 × 108 = 11340

➜ 11340 = 11340

LHS = RHS

Answer 2

★ QUESTION :

Evaluate 105 × 108 without multiplying directly.

SOULUTION :

Using the formula given below for solving this question,

➠ (x+a) (x+b) = x² + (a + b)x + ab

Here, after applying the given one, will have to substitute the values as per according to the given formula :

⟹ (x+a) (x+b) = x² + (a + b)x + ab

Considering here, the value of x = 100 , a = 5 and b = 8

⟹ (x+a) (x+b) = (100)² + (5 + 8)100 + 5 × 8

⟹ (x+a) (x+b) = 10,000 + (13)100 + 40

⟹ (x+a) (x+b) = 10,000 + 13 × 100 + 40

⟹ (x+a) (x+b) = 10,000 + 1300 + 40

⟹ (x+a) (x+b) = 11340

Therefore, After evaluating 105 × 108 without multiplying directly, i.e. using the formula of (x+a) (x+b), we got here the answer as 11,340.