Algebraic Identities and Factorisation

- (
*x*+*a*) (*x*+*b*)=*x*^{2}+ (*a*+*b*)*x*+*ab*

**Example:**

Find 206 × 198.

**Solution:**

We have,

206 × 198 = (200 + 6) (200 – 2)

= (200)^{2} + (6 + (– 2)) × 200 + (6) (– 2) [Using identity (*x* + *a*) (*x* + *b*)= *x*^{2} + (*a* + *b*) *x* + *ab*]

= 40000 + 800 – 12

= 40800 – 12

= 40788

- An identity is an equality which is true for all values of the variables in it. It helps us in shortening our calculations.
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