Special Factorizations Practice
Spot the fingerprint — difference of squares, perfect-square trinomial, sum/difference of cubes — and factor it in one step.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Difference of squares
Two squares, minus between.
Perfect-square trinomial
Middle = twice the product.
Difference of cubes
a³−b³ with SOAP signs.
Sum of cubes
a³+b³, signs flipped.
Name the pattern
Which fingerprint is it?
Prime or not?
Sum of squares never factors.
3 Watch out for these
The three mistakes students make most often on these problems.
x² + 9 = (x+3)(x+3) is wrong — that expands to x²+6x+9.
In (x−2)(x²+2x+4) the trinomial is +2x and +4 — always plus at the end.
x²+10x+25 factors instantly as (x+5)² — check first/last squares.