**Question 1.State, by writing the first four terms, the expansion of the following, where |x| < 1.(i) (1 + x)**

^{-4}Solution:

**(ii) (1 – x) ^{1/3}Solution:**

Solution:

**(iv) (1 + x) ^{-1/5}Solution:**

Solution:

**Question 2.State by writing first four terms, the expansion of the following, where |b| < |a|.**

**(ii) (a + b) ^{-4}Solution:**

**(iii) (a + b) ^{1/4}Solution:**

**(v) (a + b) ^{-1/3}Solution:**

**Question 3.Simplify the first three terms in the expansion of the following:(i) (1 + 2X)**

^{-4}Solution:

**(ii) (1 + 3x) ^{-1/2}Solution:**

**(iii) (2 – 3x) ^{1/3}Solution:**

**(iv) (5 + 4x) ^{-1/2}Solution:**

**(v) (5 – 3x) ^{-1/3}Solution:**

**Question 4.Use the binomial theorem to evaluate the following upto four places of decimals.(i) √99Solution:**

= 10 [1 – 0.005 – 0.0000125 – ……]

= 10(0.9949875)

= 9.94987 5

= 9.9499

Solution:

Solution:

**(iv) (1.02) ^{-5}Solution:**

**(v) (0.98) ^{-3}Solution:**