## Question

`If a − b = 4 and ab = 21, find the value of a`^{3} − b^{3}.

`If a − b = 4 and ab = 21, find the value of a`^{3} − b^{3}.

A. 312

B. 306

C. 316

D. 324

**Answer: C. 316**

**Solution:**

Given,

a − b = 4, ab = 21

Then,

⇒ (a − b)^{3 }**=** a^{3} − 3a^{2}b + 3ab^{2} − b^{3} **=** a^{3 }− 3ab(a − b) − b^{3}

⇒ 4^{3} = a^{3} − b^{3} − 3(21)(4)

⇒ 64 + 252 = a^{3} − b^{3}

**∴ a ^{3} − b^{3} = 316**

Hence, the answer ** a ^{3} − b^{3} = 316**.