What is the value of expression, [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}].

Option 3 : 28.89

**Given:**

Expression = [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}]

**Concepts used:**

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

a^{2} – b^{2} = (a + b) × (a – b)

**Calculation:**

Expression = [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}]

⇒ [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}] = [(25 – 12) × {25^{2} + 12^{2} + (25 × 12)}]/[(25 – 12) × (25 + 12)]

⇒ [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}] = (625 + 144 + 300)/37

⇒ [(25)^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}] = 28.89

**∴ The value of expression, [(25) ^{3} – (12)^{3}]/[(25)^{2} – (12)^{2}] is 28.89.**