Maharashtra State BoardSSC (English Medium) 7th Standard
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Factorising Binomial

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notes

Factorising a Binomial:

4, x and y are factors of every term in the binomial 4xy + 8xy2
∴ 4xy + 8xy2
= 4(xy + 2xy)2
= 4x (y + 2xy)
= 4xy (1 + 2y)

We can factorize a binomial by identifying the factors common to both terms and writing them outside the brackets in product form.

This is how we factorise 9a2bc + 12abc2

= 3(3a2bc + 4abc2)

= 3abc (3a + 4c)

(a + b)(a - b) = a2 - b2 is a formula we have already learnt.

Hence, we also get the factors a2 - b2 = (a + b) (a - b).

Example

Factorise: a2 - 4b2

a2 - 4b2

= a2 - (2b)2

= (a + 2b)(a - 2b)

Example

Factorise: 3a2 - 27b2

3a2 - 27b2

= 3(a2 - 9b2)

= 3(a + 3b)(a - 3b).

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