**If 2a – 3b = 3 and ab = 2, find the value of 8a**^{3} – 27b^{3}.

^{3}– 27b

^{3}.

**Answer :**

We know that

8a^{3} – 27b^{3} = (2a)^{3} – (3b)^{3}

According to the formula

= (2a – 3b)^{3} + 3 × 2a × 3b (2a – 3b)

By further simplification

= (2a – 3b)^{3} + 18ab (2a – 3b)

Substituting the values

= 3^{3} + 18 × 2 × 3

By further calculation

= 27 + 108

= 135

**More Solutions:**

- Prove that x2 + 1/x2 = x3 + 1/x3 = x4 + 1/x4.
- If x – 2/x = 3, find the value of x3 – 8/x3.
- If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.
- If a + 1/a = p, prove that a3 + 1/a3 = p (p2 – 3).
- If x2 + 1/x2 = 27, find the value of x – 1/x.
- Find the value of 3×3 + 5x – 3/x3 – 5/x.
- If x2 + 1/25×2 = 8 3/5, find x + 1/5x.
- If x2 + 1/4×2 = 8, find x3 + 1/8×3.
- If a2 – 3a + 1 = 0, find
- If a = 1/ (a – 5), find