Test: Algebraic identities and factorisation

Dynamic tasks on square identities, difference of squares, common factors and polynomial factorisation.

Question qty: 10
Duration in minutes: 21
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Sample questions

Expand: (x + a)2.
Factor out the common factor: ax + a·b.
Factorise: x2 − a2.
Expand: (x − a)2.
A student wrote: (x + a)2 = x2 + a2. What is the error?
Which identity correctly represents the difference of two squares?
Factorise: x2 + sx + p.
In (x + a)2 = x2 + kx + c, 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.

Test: Algebraic identities and factorisation

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Question Nr. 10 out of 10

Sample questions

Algebraic identities and factorisation

Factorisation strategy

Test: Algebraic identities and factorisation

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Algebraic identities and factorisation

Factorisation strategy

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