What is the simplified value of : (1.25)3 – 2.25 (1.25)2 + 3.75

1.	What is the simplified value of : (1.25)3 – 2.25 (1.25)2 + 3.75 (0.75)2 – (0.75)3
Answer» (1.25)³ – 2.25 (1.25)² + 3.75 (0.75)² – (0.75)³ = (1.25)³ – 3 × 0.75 × (1.25)² + 3 × 1.25 × (0.75)² – (0.75)³ = (1.25 – 0.75)³ = (0.5)³ = \(\big(\frac12\big)^3=\frac18.\) [∴ a³ - 3a²b + 3ab² - b³ = (a - b)³]

What is the simplified value of : (1.25)3 – 2.25 (1.25)2 + 3.75 (0.75)2 – (0.75)3

Answer»

(1.25)³ – 2.25 (1.25)² + 3.75 (0.75)² – (0.75)³

= (1.25)³ – 3 × 0.75 × (1.25)² + 3 × 1.25 × (0.75)² – (0.75)³

= (1.25 – 0.75)³ = (0.5)³ = \(\big(\frac12\big)^3=\frac18.\) [∴ a³ - 3a²b + 3ab² - b³ = (a - b)³]