What it does
Factorising is expanding brackets backwards: you start with 6x² − 5x − 6 and find the brackets (2x − 3)(3x + 2) that multiply to give it. This page does it step by step, the way you would write it in a test:
- ax² + bx + c: take out any common factor, look for two numbers that multiply to a × c and add to b, split the middle term, group in pairs, and write the two brackets. If the first and last terms are squares it also names the perfect-square identity (a ± b)².
- a² − b²: spot a square minus a square, as in 49x² − 16 = (7x + 4)(7x − 4).
- a³ + b³ and a³ − b³: spot two cubes and use (a + b)(a² − ab + b²) or (a − b)(a² + ab + b²).
Every answer is checked by expanding it again and by putting x = 2 into both forms. For quadratics an area picture shows the two brackets as the sides of a rectangle made of four parts.
It follows the Class 9 maths chapter on algebraic identities and the Class 10 chapters on polynomials and quadratic equations (factorising to solve).
See the identities as pictures with sliders in algebraic identity tiles; once a quadratic is factorised, its zeros are where each bracket is 0, as the polynomial zeros tool shows, and the graph is drawn in the quadratic explorer.
How to use it
- Choose the kind of expression: ax² + bx + c, a² − b² (type p and q for px² − q) or a³ ± b³ (p and q for px³ ± q, with the sign).
- Type whole numbers. The expression and its factorised form appear at the top.
- Read Step by step. If it cannot be factorised with whole numbers, the last step says why.
- New example makes a fresh one that does factorise.
- For a quadratic, As an area shows the rectangle: its width and height are the brackets, and the four parts are the terms you get when you expand.
A worked example
The page starts with 6x² − 5x − 6.
- Two numbers that multiply to a × c = 6 × (−6) = −36 and add to −5: they are −9 and 4.
- Split the middle term: 6x² − 9x + 4x − 6.
- Group in pairs: 3x(2x − 3) + 2(2x − 3) = (2x − 3)(3x + 2).
- Check: expanding gives 6x² + 4x − 9x − 6 = 6x² − 5x − 6. With x = 2 both forms give 8.
For 49x² − 16: 49x² = (7x)² and 16 = 4², so it is (7x + 4)(7x − 4). For 8x³ + 27: 8x³ = (2x)³ and 27 = 3³, so it is (2x + 3)(4x² − 6x + 9).
Tips
- Always take out a common factor first: 3x² + 6x + 3 = 3(x² + 2x + 1) = 3(x + 1)².
- If no two whole numbers work, b² − 4ac is not a perfect square and the quadratic does not split into whole-number brackets.
- The identities also help with mental arithmetic: 53² − 47² = (53 + 47)(53 − 47) = 600.
Check yourself
Four fresh questions each time: find the two numbers for a quadratic, and use identities to work out squares, a difference of squares and a cube bracket. For two numbers, type them with a comma between. Nothing is saved.
FAQ
Why only whole numbers? That is how factorising is taught at school. Quadratics with other roots are solved with the quadratic formula, as in the quadratic explorer.
Is this from the NCERT book? It covers the same topic with fibub’s own examples. fibub is not part of NCERT.
Where the numbers come from
- Algebraic identities ((a ± b)², a² − b², a³ ± b³) and factorising by splitting the middle term are standard school algebra. Written for fibub; the examples are fibub's own.
- Every answer checked against sympy.factor (x² + 7x + 12, 6x² − 5x − 6, 9x² − 12x + 4, −2x² − 14x − 24, 49x² − 16, 8x³ + 27, 2x³ − 16), and 1 400 products (px + q)(rx + s) factorised back and re-expanded exactly.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.