Combine like terms and arrange terms in descending order Algebra!

Question

(3x² -x +2 ) ( 2x³ - 3 ) =

Answer 1

This question require the "Box Method" if you're familiar with it, if not you can use the foil method. I'll show both just in case.

Box Method:

The way the box method works is that you put one of the set of parenthesis on as a column and the other as a row. Once you've done that, you multiply accordingly. For example, to fill out Column 1 Row 1, you multiply 3x² and 2x^{3 .}which is 6x⁵. We get x⁵ because since we are multiply the same variable, which is x in this case, we ADD their powers, which then becomes our new power.

3x² -x +2

2x³ 6x⁵ -2x⁴ +4x³

-3 -9x² +3x +6

Foil Method:

The way the foil method works is that you multiply one term of one set of parenthesis multiplied by the other terms in the other parenthesis. Explaining it in words sounds a lot worse than what it really is, so just let me show you instead:

(3x² - x + 2) (2x³ - 3)

3x² (2x³ - 3) - x(2x³ - 3) + 2(2x³ - 3)

All I did here was put my terms on the left parenthesis multiplied by my terms in the right parenthesis

6x⁵ - 9x² - 2x⁴ + 3x + 4x³ + 6

Now I multiplied the terms and got this. Reason we get 3x from -x times (-3) is because a negative times a negative makes a positive.

Now combine like terms if you have any (which you don't). And now, to line them up in "descending terms", we notice their powers, meaning the power of x. Our highest degree of x is 5 since we have "x⁵", and our lowest x is "x⁰" or the same as "no x". Therefore, our final answer is:

6x⁵ - 2x⁴ + 4x³ - 9x² + 3x + 6

If you know box method, is a really useful tool since you would have your terms in one "grid" and its easier to tell if you can combine like terms whereas the foil method "makes" you write them in a horizontal line and you would have to check more carefully. Both methods work and will give you the same results. Hope this made sense to you! Have a great day!

Answer 2

6x^5 - 2x^4 + 4x^3 - 9x^2 + 3x - 6