Question

Zapisz w postaci sumy algebraicznej.

a) (x+4) ^{3} + (x+4) ^{2} =

b) (x+ \frac{1}{3} ) ^{3} - (x- \frac{1}{3} ) ^{2} =

c) (2x+3) ^{3} - (x- \frac{1}{3} )^{2} =

d) (x ^{2} + x) ^{3} - (x ^{2} - x) ^{3} =

Answer 1

a) (x+4)³ + (x+4)² = x³ + 12x² + 48x + 64 + x² + 8x + 16 = x³ + 13x² + 56x + 80

b) (x+ ⅓)³ - (x- ⅓)² = x³ - x² +⅓x - ¹/₂₇ - x² + ⅔x - ¹/₉ = x³ - 2x² + x - ⁴/₂₇

c) (2x+3)³ - (x- ⅓ )²= 8x³ + 28x² + 54x + 27 - x² + ⅔x - ¹/₉ = 8x³ + 27x² + 54⅔x + 26⁸/₉

d) (x² + x)³ - (x² - x)³ = x⁶ + 3x⁵ + 3x⁴ + x³ - x⁶ + 3x⁵ - 3x⁴ + x³ = 6x⁵ + 2x³