Question

How do you combine `(5b ^ { 4} + 4b ^ { 2} + b ) - ( 2b ^ { 2} + 4b + 2b ^ { 4} )`?

Answer 1

The simplified expression is `3b^4+2b^2-3b`.

Explanation:

`(color(red)(5b^4)+color(blue)(4b^2)+color(green)(b))-(color(blue)(2b^2+color(green)(4b)+color(red)(2b^4)))`

Distribute the negative sign to the second parenthetical term and get rid of the parentheses:

`color(red)(5b^4)+color(blue)(4b^2)+color(green)(b)-color(blue)(2b^2)-color(green)(4b)-color(red)(2b^4)`

Rearrange so like terms are together:

`color(red)(5b^4)-color(red)(2b^4)+color(blue)(4b^2)-color(blue)(2b^2)+color(green)(b)-color(green)(4b)`

Combine like terms:

`color(red)(3b^4)+color(blue)(2b^2)-color(green)(3b)`