Question

What is the product of (3x-9) and 6x^2-2x+5? Write your answer in standard form.

a) Show your work.

b) Is the product of (3x-9) and 6x^2-2x+5 equal to the product of (9x-3) and 6x^2-2x+5? Explain your answer.

Answer 1

• The product of
  `3x-9` and
  `6x^2-2x+5` is
  `18x^3 -60x^2 + 33x - 45`

• No, they are not equal

Explanation:

a. Given

`3x-9` and
`6x^2-2x+5`

Required

Product

The solution is as follows

First, put both expression in different brackets

`(3x-9)(6x^2-2x+5)`

Expand
`(6x^2-2x+5)` bracket by
`(3x-9)`

To do that. we first multiply
`(6x^2-2x+5)` by 3x then by -9. This is done as follows

`3x (6x^2-2x+5) - 9(6x^2-2x+5)`

Now, we proceed to opening the bracket

`(3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)`

`(18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)`

Open both brackets

`18x^3 -6x^2+ 15x -54x^2 + 18x -45`

Collect like terms

`18x^3 -6x^2 -54x^2 + 15x + 18x -45`

`18x^3 -60x^2 + 33x - 45`

Hence, the product of
`3x-9` and
`6x^2-2x+5` is
`18x^3 -60x^2 + 33x - 45`

b. Given

• 
  `3x-9` and
  `6x^2-2x+5`

• 
  `9x-3` and
  `6x^2-2x+5`

Required

Are their products equal?

To check if they are equal or not, we find the product of both and compare the solutions

We've already solved for
`3x-9` and
`6x^2-2x+5` in the (a) part of this exercise, so we move to the product of
`9x-3` and
`6x^2-2x+5`

The solution is as follows

First, put both expression in different brackets

`(9x-3)(6x^2-2x+5)`

Expand
`(6x^2-2x+5)` bracket by
`(9x-3)`

To do that. we first multiply
`(6x^2-2x+5)` by 9x then by -3. This is done as follows

`9x (6x^2-2x+5) - 3(6x^2-2x+5)`

Now, we proceed to opening the bracket

`(9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)`

`(54x^3 - 18x^2+ 45x) - (18x^2 - 6x +15)`

Open both brackets

`54x^3 - 18x^2+ 45x -18x^2 + 6x -15`

Collect like terms

`54x^3 - 18x^2 -18x^2 + 45x + 6x -15`

`54x^3 - 36x^2 + 51x -15`

Now, we compare both answers

Is

`18x^3 -60x^2 + 33x - 45`

equal to

`54x^3 - 36x^2 + 51x -15`

No, they're not.

Reason is that, for both expressions to be equal, we must have the same expression after expanding both of them