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.
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الدليل
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 + ٣x + ٢y + ٦ = x(y + ٣) + ٢(y + ٣) = (x + ٢)(y + ٣).
a٣ + b٣ = (a + b)(a٢ − ab + b٢) and a٣ − b٣ = (a − b)(a٢ + ab + b٢). 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.