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

Answer

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

Explanation

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

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

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

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

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

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

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Subtract polynomials: x6+7x5+2x4+9x3+10x2+12x+15 , x6+9x5+8x4+9x3+12x2+15x+20.

(x6+7x5+2x4+9x3+10x2+12x+15)−(x6+9x5+8x4+9x3+12x2+15x+20)=−2x5−6x4−2x2−3x−5

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

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