You are Here: Home

# Completing the square for x3

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
1. Completing the square for x3
I am not quite sure how to do this.How do you express x^3 + 6x^2 + 10x + 4 in the form of (x+a)^3 + bx + c. I thought taking out the x would work to make it a square but it leaves me trying to square root a negative number. How do you start this question? Thanks.
2. Re: Completing the square for x3
What about expanding the RHS and the equating coefficients
3. Re: Completing the square for x3
Set 'x^3 + 6x^2 + 10x + 4 = (x+a)^3 + bx + c' and expand out the right hand side. Then you can equate coefficients, so all the x^2 terms should sum to 6 etc. Can you take it from there?
4. Re: Completing the square for x3
(Original post by TenOfThem)
What about expanding the RHS and the equating coefficients
(Original post by tory88)
Set 'x^3 + 6x^2 + 10x + 4 = (x+a)^3 + bx + c' and expand out the right hand side. Then you can equate coefficients, so all the x^2 terms should sum to 6 etc. Can you take it from there?
Thanks for your replies. Sorry for the late reply.I expanded it to ax^3 + 2a^2 x + a^3 x. I need to ask how to equate the coefficients? How do you equate the a^3 x Thanks[/QUOTE]
5. Re: Completing the square for x3
(Original post by Kj91)
Thanks for your replies. Sorry for the late reply.I expanded it to ax^3 + 2a^2 x + a^3 x. I need to ask how to equate the coefficients? How do you equate the a^3 x Thanks
6. Re: Completing the square for x3
(Original post by TenOfThem)
Thanks.So is it x^3 + 2a^2 x^2 + a^3 x. I need help as to what to do after equating them.
7. Re: Completing the square for x3
(Original post by Kj91)
Thanks.So is it x^3 + 2a^2 x^2 + a^3 x. I need help as to what to do after equating them.
Still not correct
8. Re: Completing the square for x3
Perhaps expand (x+a)^3 and find the equivalent coefficients compared to the full one to see if there is a sort of pattern?

I haven tried this, I may try this later
9. Re: Completing the square for x3
(Original post by Kj91)
Thanks.So is it x^3 + 2a^2 x^2 + a^3 x. I need help as to what to do after equating them.
Expand (x+a)^2, then multiply the whole thing by (x+a). What do you get?
10. Re: Completing the square for x3
(Original post by tory88)
Expand (x+a)^2, then multiply the whole thing by (x+a). What do you get?
11. Re: Completing the square for x3
(Original post by tory88)
Expand (x+a)^2, then multiply the whole thing by (x+a). What do you get?
This is what I get.

(x+a)(x+a)

x^2 + 2ax + a^2

x(x^2 + 2ax + a^2) = x^3 + 2a x^2 + a^2 x)

a(x^3 + 2a x^2 + a^2 x) = ax^3 + 2a^2 x^2 + a^3 x + bx + c

Once I equal this to this to x^3 + 6x^2 + 10x + 4. I am unsure how to equate.
Last edited by Kj91; 01-08-2012 at 18:15.
12. Re: Completing the square for x3
(Original post by Kj91)
This is what I get.

x(x^2 + 2ax + a^2) = x^3 + 2a x^2 + a^2 x)

a(x^3 + 2a x^2 + a^2 x) = ax^3 + 2a^2 x^2 + a^3 x + bx + c
This is wrong

when you times by (x+a) you do not times by x and then times by a

I do not normally do full solutions but hold on and I will show you this
13. Re: Completing the square for x3
here is the bracket cubed

then do not forget to add the bx + c

then equate coefficients

Last edited by TenOfThem; 01-08-2012 at 18:25.
14. Re: Completing the square for x3
(Original post by TenOfThem)
here is the bracket cubed

then do not forget to add the bx + c

then equate coefficients

Thanks very much for taking the time to post a solution to this question. I get it now. I'll need to go over some more questions like this.
15. Re: Completing the square for x3
(Original post by Kj91)
Thanks very much for taking the time to post a solution to this question. I get it now. I'll need to go over some more questions like this.
No problem

You need to practice some of your basic algebra and feel totally secure

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Last updated: August 1, 2012
Study resources