Question

Find: (6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6)

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 $7m^5-3m^3-3$.