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.

Answer 1

Given:

The expression is:

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

To find:

The resulting polynomial in standard form.

Solution:

We have,

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

Write subtraction of a polynomial expression as addition of the additive inverse.

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

Rewrite terms that are subtracted as addition of the opposite.

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

Group like terms.

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

Combine like terms.

`7m^5+(-3)+(-3m^3)+0`

On simplification, we get

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

Write the polynomial in standard form.

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

Therefore, the required polynomial in standard form is
`7m^5-3m^3-3`.