15.4k views
1 vote
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.

User Ujell
by
4.9k points

1 Answer

7 votes

Answer:

  • 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

User Anton Gaenko
by
5.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.