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**Exercise 8.1**

**Expand each of the expression in Exercises 1 to 5.**

**1. **

**Ans. **Using Binomial Theorem,

=

=

**2. **

**Ans. **Using Binomial Theorem,

=

=

**3. **

**Ans. **Using Binomial Theorem,

=

=

**4. **

**Ans. **Using Binomial Theorem,

=

=

**5. **

**Ans. **Using Binomial Theorem,

=

=

**Using binomial theorem evaluate each of the following:**

**6. **

**Ans. **Given:

Using Binomial Theorem,

=

= 1000000 – 120000 + 4800 – 64

= 1004800 – 120064 = 884736

**7. **

**Ans. **Given:

Using Binomial Theorem,

=

= 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32

= 11040808032

**8. **

**Ans. **Given:

Using Binomial Theorem,

=

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401

**9. **

**Ans. **Given:

Using Binomial Theorem,

=

= 10000000000 – 500000000 + 10000000 – 100000 + 500 – 1

= 9509900499

**10. Using binomial theorem, indicate which number is larger **** or 1000.**

**Ans. **Given:

Using Binomial Theorem,

= 1 + 10000 (0.1) + other positive numbers

= 1 + 1000 + other positive numbers

which is greater than 1000

**11. Find **** Hence evaluate: **

**Ans. **Given:

Using Binomial Theorem,

=

=

=

Putting and

=

**12. Find **** Hence or otherwise evaluate **

**Ans. **Given:

Using Binomial Theorem,

=

= =

Putting

=

= 2 [ 8 + 60 + 30 + 1] = = 198

**13. Show that **** is divisible by 64 whenever **** is a positive integer.**

**Ans. **Given:

Using Binomial Theorem,

=

=

which shows that is divisible by 64.

**14. Prove that **

**Ans. **L.H.S. =

=

= = R.H.S.

Good solutions