Simplify:(i) a2 (2a – 1) + 3a + a3 – 8(ii) 3/2x2 (x2 – 1) + 1/4x

1.	Simplify:(i) a2 (2a – 1) + 3a + a3 – 8(ii) 3/2x2 (x2 – 1) + 1/4x2 (x2 + x) – 3/4x (x3 – 1)
Answer» (i) a² (2a – 1) + 3a + a³ – 8 = 2a³ – a²+ 3a + a³ – 8 = 3a³ – a² + 3a – 8 (ii) 3/2x² (x² – 1) + 1/4x² (x² + x) – 3/4x (x³ – 1) = 3/2x⁴ – 3/2x² + 1/4x⁴ + 1/4x³ – 3/4x⁴ + 3/4x = 3/2x⁴ + 1/4x⁴ – 3/4x⁴ – 3/2x² + 1/4x³ + 3/4x = 4/4x⁴ + 1/4x³ – 3/2x² + 3/4x = x⁴ + 1/4x³ – 3/2x² + 3/4x

Simplify:(i) a2 (2a – 1) + 3a + a3 – 8(ii) 3/2x2 (x2 – 1) + 1/4x2 (x2 + x) – 3/4x (x3 – 1)

Answer»

(i) a² (2a – 1) + 3a + a³ – 8

= 2a³ – a²+ 3a + a³ – 8

= 3a³ – a² + 3a – 8

(ii) 3/2x² (x² – 1) + 1/4x² (x² + x) – 3/4x (x³ – 1)

= 3/2x⁴ – 3/2x² + 1/4x⁴ + 1/4x³ – 3/4x⁴ + 3/4x

= 3/2x⁴ + 1/4x⁴ – 3/4x⁴ – 3/2x² + 1/4x³ + 3/4x

= 4/4x⁴ + 1/4x³ – 3/2x² + 3/4x

= x⁴ + 1/4x³ – 3/2x² + 3/4x