Test
Algebraic identities and factorisation
Dynamic tasks on square identities, difference of squares, common factors and polynomial factorisation.
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Sample questions
- Expand: (x + ___)2.
- Expand: (x − ___)2.
- Factorise: x2 − ___2.
- Factor out the common factor: ___x + ___·___.
- In (x + ___)2 = x2 + kx + ___, find coefficient k.
Algebraic identities and factorisation
The identities (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and a² − b² = (a − b)(a + b) help expand and factor expressions efficiently. The middle term of a squared binomial is always twice the product.
Factorisation strategy
First take out any common factor. Then look for a difference of squares or a perfect-square trinomial. Check the result by multiplying the factors back out; sign errors usually appear in the middle term.
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