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

Answer:

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

• No, they are not equal

Step-by-step 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