# Evaluate the following using suitable identities:

(i) (99)^{3 }(ii) (102)^{3 }(iii) (998)^{3}

**Solution:**

We will use the following algebraic Identities to evaluate the given expressions.

(x + y)^{3} = x^{3} + y^{3} + 3xy(x + y)

(x - y)^{3} = x^{3} - y^{3} - 3xy(x - y)

**(i)** (99)^{3} = (100 - 1)^{3}

Identity: Here we can use (x - y)^{3} = x^{3} - y^{3} - 3xy(x - y)

Let us substitute x = 100, y = 1

(99)^{3} = (100)^{3} - (1)^{3} - 3(100)(1)(100 - 1)

= 1000000 - 1 - 300 × 99

= 999999 - 29700

= 970299

**(ii)** (102)^{3} = (100 + 2)^{3}

Identity: (x + y)^{3} = x^{3} + y^{3} + 3xy(x + y)

Let us substitute x = 100, y = 2

(102)^{3} = (100)^{3} + (2)^{3} + 3(100)(2)(100 + 2)

= 1000000 + 8 + 600 × 102

= 1000008 + 61200

= 1061208

**(iii)** (998)^{3} = (1000 - 2)^{3}

Identity: (x - y)^{3} = x^{3} - y^{3} - 3xy(x - y)

Let us substitute x = 1000, y = 2

(998)^{3} = (1000)^{3} - (2)^{3} - 3(1000) (2) (1000 - 2)

= 1000000000 - 8 - 6000 × 998

= 999999992 - 5988000

= 994011992

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 2

**Video Solution:**

## Evaluate the following using suitable identities: (i) (99)³^{ }(ii) (102)³^{ }(iii) (998)³

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 7:

**Summary:**

The evaluated values of the following (99)^{3}, (102)^{3}, and (998)^{3} using suitable identities are 970299, 1061208, and 994011992 respectively.

**☛ Related Questions:**

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