[Kj91]

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.

[TenOfThem]

What about expanding the RHS and the equating coefficients

[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?

[Kj91]

(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]

[TenOfThem]

(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

Your expansion is incorrect

[Kj91]

(Original post by TenOfThem)
Your expansion is incorrect

Thanks.So is it x^3 + 2a^2 x^2 + a^3 x. I need help as to what to do after equating them.

[TenOfThem]

(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

[Dmon1Unlimited]

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

[tory88]

(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?

[TenOfThem]

(Original post by tory88)
Expand (x+a)^2, then multiply the whole thing by (x+a). What do you get?

And then do not forget to add on your bx+c

[Kj91]

(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.

[TenOfThem]

(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

[TenOfThem]

here is the bracket cubed



then do not forget to add the bx + c



then equate coefficients

[Kj91]

(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.

[TenOfThem]

(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