To factorise the expression 2x³ + 54y³ + 4x + 12y, we need to look for common factors and group the terms effectively.
First, we can group the terms:
- 2x³ + 4x
- 54y³ + 12y
Now, let’s factor out the common factors from each group:
- For the first part, 2x³ + 4x: we can factor out 2x, giving us:
- 2x(x² + 2)
- For the second part, 54y³ + 12y: we can factor out 6y, giving us:
- 6y(9y² + 2)
So the expression now looks like:
2x(x² + 2) + 6y(9y² + 2)
At this point, we should check if we can factor further by looking for common terms or patterns between the groups. However, these two groups do not share a common factor, and the polynomials within the brackets do not factor nicely either.
Thus, the factorised expression is:
2x(x² + 2) + 6y(9y² + 2)
This is as simplified as we can get for the given expression. Always remember to look for common factors first and try to group the terms for easier factorisation.