Grouping and cubes: factorising
Factorise a four-term polynomial by grouping, factorise sums and differences of cubes and choose where to start when several methods fit.
- Ukraine: grade 7
Guide
Ukrainian Algebra 7 (§§ 13, 18, 19) teaches these: the grouping method, the sum and difference of cubes, and using different methods together.
Grouping: put the terms in groups, take the common factor out of each group, then take out the common bracket. xy + 3x + 2y + 6 = x(y + 3) + 2(y + 3) = (x + 2)(y + 3).
a3 + b3 = (a + b)(a2 − ab + b2) and a3 − b3 = (a − b)(a2 + ab + b2). The second factor is an incomplete square of a sum or difference: it has no doubled product.
When several methods fit: take out a common factor first, then look for a formula (difference of squares, sum or difference of cubes, square of a binomial), and group only after that.
Tap a chip, then «Split». The chip splits into the factors the task gives. Then type the product with brackets.