Expanding Brackets Part 2

Video

Video Explanation (Expanding three brackets)


(ON THIS PAGE we have used X to symbolise the multiplication sign, so you don't confuse it with x which is the term in the bracket)
If you do not know how to expand brackets, please read the expanding brackets part 1 page first.
Expanding three brackets is just a step by step process, if you can expand 2 brackets. Lets get into understanding the question in the video.
Question (x + 2)(x + 3)(2x + 1)
First lets understand what this means.
(x + 2)(x + 3)(2x + 1) = (x + 2) X (x + 3) X (2x + 1)
So we can break apart the question, we can find what (x + 2)(x + 3) equals and then multiply the answer with (2x + 1)
So
(x + 2)(x + 3) = x2 + 3x + 2x + 6 = x2 + 5x + 6
So
(x + 2)(x + 3)( 2x + 1) = (x2 + 5x + 6)(2x + 1)
Now lets multiply each term from the first bracket with each term in the second bracket.
x2 X 2x = 2x3x2 X 1 = x2
5x X 2x = 10x25x X 1 = 5 X x X 1 = 5x
6 X 2x = 12x6 X 1 = 6
So
(x2 + 5x + 6)(2x + 1) = 2x3 + x2 + 10x2 + 5x + 12x + 6 (This can be simplified)
 2x3 + x2 + 10x2 + 5x + 12x + 6 = 2x3 + 11x2 + 17x + 6
One point to take into consideration is that the question asks us to expand
(x + 2)(x + 3)(2x + 1), we chose to expand (x + 2)(x + 3) first, then multiply the result of the expansion with (2x + 1).
Remember that (x + 2)(x + 3)(2x + 1) = (x + 2) X (x + 3) X (2x + 1)
We could of found the product of (2x + 1)(x + 2) first, then multiplied the product with (x + 3). So it does not matter what brackets you multiply first.

Try this question

  1. Expand (2x - 5)(3 + x)(-x + 5)

Answer

  1. Expand (2x - 5)(3 + x)(-x + 5)

Lets perform (2x - 5)(3 + x) first

(2x - 5)(3 + x) = 6x + 2x2 -15 -5x = x + 2x2 -15

Multiply the product with the remaining bracket, in our case this is (-x + 5).

(x + 2x2 - 15)(-x + 5) = (-x + 5)(x + 2x2 -15) =

-x2 - 2x3 + 15x + 5x + 10x2 - 75 =

-2x3 + 9x2 + 20x -75 (SIMPLIFIED)