Difference of two squares

Remove the brackets from:

\((a - b)(a + b)\)

\(= {a^2} + ab - ab - {b^2}\)

\(= {a^2} - {b^2}\)

If we reverse this, we say that:

\({a^2} - {b^2} = (a - b)(a + b)\)

Therefore to factorise an expression that is the difference of two squares, we say that:

\({a^2} - {b^2} = (a - b)(a + b)\)

Example one

Factorise the following:

\({x^2} - 16\)

Look out for square numbers.

\(= {(x)^2} - {(4)^2}\)

\(= (x - 4)(x + 4)\)

Example two

Factorise the following:

\(25{p^2} - 1\)

Get into the form \({(..)^2} - {(..)^2}\)

\(= {(5p)^2} - {(1)^2}\)

\(= (5p - 1)(5p + 1)\)

Question

Factorise the following:

\(16 - {w^2}\)

Question

Factorise the following:

\({y^2} - 81\)

Question

Factorise the following

\(36{f^2} - 49{g^2}\)

Question

Factorise the following:

\(3{a^2} - 27\)

Factorising trinomials

Factorising quadratics

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Factorising an algebraic expressionDifference of two squares