Solutions

Problem Set 3

Algebra

In each case expand and collect like terms

a) x⁶(x² + 1)² =x⁶(x² + 1) (x²+1) = x⁶(x⁴ + 2x²+1) = x¹⁰ + 2x⁸ + x⁶

b) x(x – 9)(x + 1) = x(x² – 8x -9) =x³ -8x² – 9x

c) x⁴ (x²-2)(x-1) =x⁴(x³ –x² -2x + 2) = x⁷ –x⁶ – 2x⁵ + 2x⁴

d) (x + 1)³ =(x+1)(x +1)(x + 1) = (x+1)(x² + 2x + 1) =x³ + 2x² + x + x² + 2x + 1 = x³ +3x² + 3x + 1

e) x³(x – 9)(x+9) =x³ (x² - 81) = x⁵ – 81x³