Question

How do you combine like terms in `4p ^ { 4} + 7p ^ { 2} - 3p ^ { 3} - 8- 3p ^ { 2} - 2p ^ { 4} - 8- 3p ^ { 2} - 2p ^ { 4}`?

Answer 1

`4p^4 +7p^2-3p^3-8 -3p^2 -2p^4 -8-3p^2 -2p^4`

`=4color(magenta)(p^4) +7color(blue)(p^2)-3color(lime)(p^3)color(darkorange)(-8) -3color(blue)(p^2) -2color(magenta)(p^4) color(darkorange)(-8)-3color(blue)(p^2) -2color(magenta)(p^4)`

`=color(lime)(-3p^3) color(blue)(+p^2) color(darkorange)(-16)`

Explanation:

All of the algebraic terms have the variable `p`, but the indices are different. Find all of the terms which have the same power of `p`.

`4color(magenta)(p^4) +7color(blue)(p^2)-3color(lime)(p^3)color(darkorange)(-8) -3color(blue)(p^2) -2color(magenta)(p^4) color(darkorange)(-8)-3color(blue)(p^2) -2color(magenta)(p^4)`

Collect all the like terms together.

`=color(magenta)(4p^4-2p^4-2p^4) color(lime)(-3p^3) color(blue)(+7p^2-3p^2-3p^2) color(darkorange)(-8-8)`

Add the co-efficients but keep the powers the same.

`=color(magenta)(0p^4) color(lime)(-3p^3) color(blue)(+p^2) color(darkorange)(-16)`

Answer 2

See a solution process below:

Explanation:

First, group the like terms:

`4p^4 - 2p^4 - 2p^4 - 3p^3 + 7p^2 - 3p^2 - 3p^2 - 8 - 8`

Now, combine like terms:

`(4 - 2 - 2)p^4 - 3p^3 + (7 - 3 - 3)p^2 + (-8 - 8)`

`0p^4 - 3p^3 + 1p^2 + (-16)`

`-3p^3 + p^2 - 16`