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Question
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
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Solution
`(2x + 1/3)^2 - (x - 1/2)^2 = [(2x + 1/3) - (x - 1/2)][(2x + 1/3) + (x - 1/2)]`
= `(2x - x + 1/3 + 1/2)(2x + x + 1/3 - 1/2)` ...[Using identity, a2 – b2 = (a – b)(a + b)]
= `(x + (2 + 3)/6)(3x + (2 - 3)/6)`
= `(x + 5/6)(3x - 1/6)`
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