Question

How do you simplify `(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)`?

Answer 1

`x^3+6x^2+2x+13`

Explanation:

Write as:`" "+1(6x^2-3+5x^3) -1(4x^3-2x-16)`

The 1's in front of the brackets are not normally written.
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`color(blue)("Multiply everything inside the left brackets by +1")`

`6x^2-3+5x^3`

Ordering these gives

`color(blue)(5x^3+6x^2-3)`

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`color(blue)("Multiply everything inside the right brackets by -1")`

`color(blue)(-4x^3+2x+16)`
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`color(blue)("Putting everything together")`

`5x^3+6x^2-3" "-4x^3+2x+16`

Collecting like terms:

`(5x^3-4x^3)+6x^2+2x+(16-3)`

`color(blue)(x^3+6x^2+2x+13)`