Question

How do you simplify `5(w²-6)-8[9-(w²+6)]`?

Answer 1

The final answer is `13w^2-54`

Explanation:

One thing to remember when you are simplifying polynomials is that if you are multiplying terms in the bracket by a number, multiply it with all the terms inside the bracket.

Also if you have a negative or minus outside of a bracket, you have to distribute it to all terms inside the bracket.

`5(w^2-6)-8[9-(w^2+6)]`

Start off with the terms with brackets. Distribute the `5` with all the terms inside the bracket in the first term.

`5w^2-30-8[9 -(w^2+6)]`

Get rid of the brackets inside the second term by distributing the minus across the terms in the bracket.

`5w^2-30-8(9 -w^2-6)`

You can then subtract the like terms in the bracket

`5w^2-30-8(-w^2+3)`

Now multiply the `-8` with all of the terms in the bracket.

`5w^2-30+8w^2-24`

You can now add and subtract the like terms in the expression.

`13w^2-54`

Answer 2

See the entire simplification process below:

Explanation:

First, eliminate the parentheses within the brackets. Be careful to handle the signs of the individual terms correctly:

`5(w^2 - 6) - 8[9 - color(red)((w^2 + 6))]`

`5(w^2 - 6) - 8[9 - color(red)(w^2) - color(red)(6)]`

Next, expand the terms within parentheses by multiplying the terms within parentheses/brackets by the term outside the parentheses/bracket. Again, be careful to handle the signs of the individual terms correctly:

`color(red)(5)(w^2 - 6) - color(blue)(8)[9 - w^2 - 6]`

`(color(red)(5) xx w^2) - (color(red)(5) xx 6) - (color(blue)(8) xx 9) + (color(blue)(8) xx w^2) + (color(blue)(8) xx 6)`

`5w^2 - 30 - 72 + 8w^2 + 48`

Now, group and then combine like terms:

`5w^2 + 8w^2 - 30 - 72 + 48`

`(5 + 8)w^2 - 54`

`13w^2 - 54`