Subtract polynomials: $s^{6} + 7 s^{5} + 2 s^{4} + 9 s^{3} + 10 s^{2} + 12 s + 15$ , $s^{6} + 9 s^{5} + 8 s^{4} + 9 s^{3} + 12 s^{2} + 15 s + 20$ .

Answer

$(s^{6} + 7 s^{5} + 2 s^{4} + 9 s^{3} + 10 s^{2} + 12 s + 15) - (s^{6} + 9 s^{5} + 8 s^{4} + 9 s^{3} + 12 s^{2} + 15 s + 20) = - 2 s^{5} - 6 s^{4} - 2 s^{2} - 3 s - 5$

Explanation

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

- s^{6} s^{6} 7 s^{5} 9 s^{5} 2 s^{4} 8 s^{4} 9 s^{3} 9 s^{3} 10 s^{2} 12 s^{2} 12 s 15 s 1520

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

- s^{6} - s^{6} 7 s^{5} - 9 s^{5} 2 s^{4} - 8 s^{4} 9 s^{3} - 9 s^{3} 10 s^{2} - 12 s^{2} 12 s - 15 s 15 - 20

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

- s^{6} - s^{6} 2 s^{6} 7 s^{5} - 9 s^{5} 16 s^{5} 2 s^{4} - 8 s^{4} 10 s^{4} 9 s^{3} - 9 s^{3} 18 s^{3} 10 s^{2} - 12 s^{2} 22 s^{2} 12 s - 15 s 27 s 15 - 20 35

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Subtract polynomials: s6+7s5+2s4+9s3+10s2+12s+15 , s6+9s5+8s4+9s3+12s2+15s+20.

(s6+7s5+2s4+9s3+10s2+12s+15)−(s6+9s5+8s4+9s3+12s2+15s+20)=−2s5−6s4−2s2−3s−5

Subtract polynomials: $s^{6} + 7 s^{5} + 2 s^{4} + 9 s^{3} + 10 s^{2} + 12 s + 15$ , $s^{6} + 9 s^{5} + 8 s^{4} + 9 s^{3} + 12 s^{2} + 15 s + 20$ .

$(s^{6} + 7 s^{5} + 2 s^{4} + 9 s^{3} + 10 s^{2} + 12 s + 15) - (s^{6} + 9 s^{5} + 8 s^{4} + 9 s^{3} + 12 s^{2} + 15 s + 20) = - 2 s^{5} - 6 s^{4} - 2 s^{2} - 3 s - 5$