Question

Subtract polynomials: $20 s^{7} + 360 s^{6} + 2700 s^{5} + 11200 s^{4} + 27480 s^{3} + 37440 s^{2} + 21600 s$ , $s^{7} + 36 s^{6} + 512 s^{5} + 3634 s^{4} + 13287 s^{3} + 22730 s^{2} + 12600 s$ .

Answer

$(20 s^{7} + 360 s^{6} + 2700 s^{5} + 11200 s^{4} + 27480 s^{3} + 37440 s^{2} + 21600 s) - (s^{7} + 36 s^{6} + 512 s^{5} + 3634 s^{4} + 13287 s^{3} + 22730 s^{2} + 12600 s) = 19 s^{7} + 324 s^{6} + 2188 s^{5} + 7566 s^{4} + 14193 s^{3} + 14710 s^{2} + 9000 s$

Explanation

Step 1: Write second polynomial below the first one. Making sure like terms are lined up.

- 20 s^{7} s^{7} 360 s^{6} 36 s^{6} 2700 s^{5} 512 s^{5} 11200 s^{4} 3634 s^{4} 27480 s^{3} 13287 s^{3} 37440 s^{2} 22730 s^{2} 21600 s 12600 s

Step 2: Change ALL the signs in the second row.

- 20 s^{7} - s^{7} 360 s^{6} - 36 s^{6} 2700 s^{5} - 512 s^{5} 11200 s^{4} - 3634 s^{4} 27480 s^{3} - 13287 s^{3} 37440 s^{2} - 22730 s^{2} 21600 s - 12600 s

Step 3: Combine like terms (add each column):

- 20 s^{7} - s^{7} 21 s^{7} 360 s^{6} - 36 s^{6} 396 s^{6} 2700 s^{5} - 512 s^{5} 3212 s^{5} 11200 s^{4} - 3634 s^{4} 14834 s^{4} 27480 s^{3} - 13287 s^{3} 40767 s^{3} 37440 s^{2} - 22730 s^{2} 60170 s^{2} 21600 s - 12600 s 34200 s

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