Factorizing Calculator
Type an expression and see each step.
The rules
1. Perfect square trinomiala² ± 2ab + b² = (a ± b)²First and third terms are perfect squares. Middle term = ± 2 × √first × √third.
2. Difference of two squaresa² − b² = (a − b)(a + b)Two terms, both perfect squares, with a minus between them.
3. Finding a missing term (use the K key)Middle = ± 2 × √first × √thirdFirst = (middle)² ÷ (4 × third)Third = (middle)² ÷ (4 × first)
4. Sum and difference of cubesa³ + b³ = (a + b)(a² − ab + b²)a³ − b³ = (a − b)(a² + ab + b²)Small bracket and big bracket. The middle sign in the big bracket changes.
5. GCF firstGCF × (what is left)Always take out the greatest common factor first, then check the bracket again.
6. Trinomial x² + bx + c(x + m)(x + n), where m × n = c and m + n = bMake attempts until the product and the sum both work.
7. Grouping (four terms)a(x + y) + b(x + y) = (x + y)(a + b)Group in pairs, take out each pair’s GCF, then the common bracket.
8. Perfect square minus a square(x − y)² − c² = (x − y − c)(x − y + c)Group three terms into a perfect square, then use the difference of two squares.
9. Trinomial where the middle term does not fitb⁴ + 5b² + 9 = (b² + 3)² − b² = (b² + 3 − b)(b² + 3 + b)Take the square roots of the first and third terms: b² and 3. The perfect square (b² + 3)² has the middle term 6b², so take away the extra b². Then use the difference of two squares.
10. Completing the square (sum of two squares)m⁴ + 64 = (m² + 8)² − 16m² = (m² + 8 − 4m)(m² + 8 + 4m)Both terms are perfect squares with a plus between them. Make the perfect square (m² + 8)², take away its middle term 16m² (2 × m² × 8), write 16m² as (4m)², then use the difference of two squares.
Factorizing Calculator
Keys: x² and xⁿ for powers, a/b for fractions, √ and ∛ for roots of a single term, e.g. √(49b²). Add = to solve an equation, e.g. x²−25=0. Decimals work too. Use K for a missing term, e.g. 4x²+K+9. Numbers work too: 25²−15² or 52×48.