How do I factorise this cubic expression?

  • Thread starter physicsfun_12
  • Start date
Then, factor (x+2y) from the first group and (x+3y) from the last group.In summary, to factorize the cubic expression x^3+3x^2y+2xy^2+6y^3, group the terms together and factor each group. Then, factor out common terms from each group, resulting in the expression (x+2y)(x+3y)(x+2y+3y).
  • #1
physicsfun_12
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0

Homework Statement


Hello there, hope you'r well.

I am having trouble factorising this cubic. I am comfortable with quadratics however I have never had to factorise anything to the power 3 before.

x^3+3x^2y+2xy^2+6y^3

Thanks in advance for any input.

Mike


Homework Equations


n/a


The Attempt at a Solution


I have had ago but didn't get very far!

(3x+2y)(xy) that does the bit in the middle, excluding the two terms to the power 3.

Thanks again for any help with this.

Mike
 
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  • #2
physicsfun_12 said:
x^3+3x^2y+2xy^2+6y^3

Hi Mike! :smile:

(try using the X2 tag just above the Reply box :wink:)

Assuming it has rational roots, they must be x/y = ± 1 or 2 or 3 or 6, so just try all of them. :biggrin:

(to save time, do the "odd" terms together, and the "even" terms together :wink:)
 
  • #3
Try grouping the first two and last two terms together and factor each group. Then...
 
  • #4
Factor x2 from the first two terms and 2y2 from the last two terms.
 

1. What is factorisation of cubics?

Factorisation of cubics is a method used in algebra to break down a cubic equation into simpler factors. This allows for easier solving of the equation and finding its roots.

2. Why is factorisation of cubics useful?

Factorisation of cubics is useful because it allows for the simplification of complex equations, making them easier to solve. It also helps in finding the roots of the equation, which can have real or complex values.

3. What is the general formula for factorisation of cubics?

The general formula for factorisation of cubics is (x-a)(x-b)(x-c), where a, b, and c are the roots of the equation. This formula is derived from the fact that the sum of the roots of a cubic equation is equal to the negative coefficient of the quadratic term.

4. How do you know when a cubic equation can be factorised?

A cubic equation can be factorised if it has three distinct roots. This can be determined by finding the discriminant of the equation, which is the expression under the square root sign in the quadratic formula. If the discriminant is greater than zero, the equation can be factorised.

5. Can all cubic equations be factorised?

No, not all cubic equations can be factorised. Some equations may have complex roots or may not have any real roots at all. In these cases, the equation cannot be factorised using real numbers. However, it is possible to factorise any cubic equation using complex numbers.

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