find: $(6m^{5}+3 - m^{3}-4m)-(-m^{5}+2m^{3}-4m + 6)$\n1. write subtraction of a polynomial expression as…

find: $(6m^{5}+3 - m^{3}-4m)-(-m^{5}+2m^{3}-4m + 6)$\n1. write subtraction of a polynomial expression as addition of the additive inverse.\n$(6m^{5}+3 - m^{3}-4m)+(m^{5}-2m^{3}+4m - 6)$\n2. rewrite terms that are subtracted as addition of the opposite.\n$6m^{5}+3+(-m^{3})+(-4m)+m^{5}+(-2m^{3})+4m+(-6)$\n3. group like terms.\n$6m^{5}+m^{5}+3+(-6)+(-m^{3})+(-2m^{3})+(-4m)+4m$\n4. combine like terms.\n5. write the resulting polynomial in standard form.\n$\\underline{\\hspace{2cm}}m^{5}-\\underline{\\hspace{2cm}}m^{3}+\\underline{\\hspace{2cm}}m - 3$

find: $(6m^{5}+3 - m^{3}-4m)-(-m^{5}+2m^{3}-4m + 6)$\n1. write subtraction of a polynomial expression as addition of the additive inverse.\n$(6m^{5}+3 - m^{3}-4m)+(m^{5}-2m^{3}+4m - 6)$\n2. rewrite terms that are subtracted as addition of the opposite.\n$6m^{5}+3+(-m^{3})+(-4m)+m^{5}+(-2m^{3})+4m+(-6)$\n3. group like terms.\n$6m^{5}+m^{5}+3+(-6)+(-m^{3})+(-2m^{3})+(-4m)+4m$\n4. combine like terms.\n5. write the resulting polynomial in standard form.\n$\\underline{\\hspace{2cm}}m^{5}-\\underline{\\hspace{2cm}}m^{3}+\\underline{\\hspace{2cm}}m - 3$

Answer

Explanation:

Step1: Combine like - terms for $m^5$

$6m^5+m^5=(6 + 1)m^5=7m^5$

Step2: Combine like - terms for $m^3$

$-m^3-2m^3=(-1-2)m^3=-3m^3$

Step3: Combine like - terms for $m$

$-4m + 4m=0m = 0$

Step4: Combine constant terms

$3-6=-3$

Answer:

$7m^5-3m^3+0m - 3$ which simplifies to $7m^5-3m^3-3$ (the blanks should be filled with 7, 3, 0 respectively)