Given -

105 × 98

To -

SIMPLIFY using suitable Algebraic identity.

Solution -

→ (100 + 5)(100 - 2)

Using 5TH identity of Algerbraic identites which is = (x + a) (x + b) = x² + (a + b)x + (a × b)

Substituting the values -

(100 + 5)(100 -2) = (100)² + (5 + (-2))100 + (5 × -2)

→ 10000 + 300 - 10

Value of 105 × 98 = 10290.

Procedure :-

• This question is from Algebraic identites.

• In this question we are given with the 150 × 98, and we have to simplify it by using an Algerbraic identity, for that we will add 5 in 100 to 105 and subract 2 from 100 to MAKE it 98.

• After that it will give us another Expression (100 + 5)(100-2). As you know that we have an Indentity related to it (x + a)(x + b) = x² + (a + b)x + (a × b).

• Then we will equate the whole expression then the final answer is 10000 + 300 - 10.

Other Algebraic identites -

1. (a + b)² = a² + 2ab + b²

2. (a - b)² = a² - 2ab + b²

3. (a + b)(a - b) = a² - b²

4. (x + a)(x + b) = x² + (a + b)x + (a × b)

5. (a + b + c)² = a² + b² + c² + 2ab + 2BC + 2ca.

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