Question

Find: (6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6) Write subtraction of a polynomial expression as addition of the additive inverse. (6m5 + 3 – m3 – 4m) + (m5 – 2m3 + 4m – 6) Rewrite terms that are subtracted as addition of the opposite. 6m5 + 3 + (–m3) + (–4m) + m5 + (–2m3) + 4m + (–6) Group like terms. [6m5 + m5] + [3 + (–6)] + [(–m3) + (–2m3)] + [(–4m) + 4m] Combine like terms. Write the resulting polynomial in standard form. m5 – m3 + m – 3

Answer 1

`7m^5-3m^3-3`

Explanation:

Given expression

`(6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)`

Write subtraction of a polynomial expression as addition of the additive inverse .Therefore we can write expression as

`(6m^5+3-m^3-4m)+(m^5-2m^3+4m-6)`

Rewrite terms that are subtracted as addition of the oppostite .Therefore , we can write expression as

`6m^5+3+(-m^3)+ (-4m)+m^5+(-2m^3)+4m+(-6)`

Grouping og like terms . Then we get the expession is given by

`[6m^5+m^5]+[3+(-6)]+[(-m^3)+(-2m^3)]+[(-4m)+4m]`

Combine like terms then we can write expression

`7m^5-3-3m^3`

Write the resulting polynomial in standard form

`&m^5-m^3 -3`.

(6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)=m^5-m^3-3.

Answer 2

Exactly right down to the last step, but some errors in combining terms.

(6m^5 + 3 – m^3 – 4m) – (–m^5 + 2m^3 – 4m + 6)
= (6m^5 + 3 – m^3 – 4m) + (m^5 – 2m^3 + 4m – 6)
= 6m^5 + 3 + (–m^3) + (–4m) + m^5 + (–2m^3) + 4m + (–6)
= [6m^5 + m^5] + [3 + (–6)] + [(–m^3) + (–2m^3)] + [(–4m) + 4m]
= (6+1)m^5 +(-1-2)m^3 +(-4+4)m +(3-6)
= 7m^5 – 3m^3 – 3