Eric Nicholas K's answer to Wesley's Secondary 3 A Maths Singapore question.
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Part a
Date Posted:
4 years ago
The factorisation of a3 - b3 is (a - b) (a2 + ab + b2).
So we call a3 - b3 the expanded form and (a - b) (a2 + ab + b2) the factorised form.
So in this case,
64 - (x + 1)^3 is considered the “expanded form” and
[4 - (x + 1)] [4^2 + 4 (x + 1) + (x + 1)^2] the “factorised form”.
Having said that, leaving the second bracket just like that is considered not simplified, so we must tidy up the second term by expanding its contents and leaving our answer as ax2 + bx + c.
It’s a matter of judgement to see whether an expression is considered “simplified” or not.
Things like x^2 - 1 are not considered simplified because they are not factorised, but things like (x + 3)^2 + 2 (x - 4) + 7 are also not considered simplified.
So we call a3 - b3 the expanded form and (a - b) (a2 + ab + b2) the factorised form.
So in this case,
64 - (x + 1)^3 is considered the “expanded form” and
[4 - (x + 1)] [4^2 + 4 (x + 1) + (x + 1)^2] the “factorised form”.
Having said that, leaving the second bracket just like that is considered not simplified, so we must tidy up the second term by expanding its contents and leaving our answer as ax2 + bx + c.
It’s a matter of judgement to see whether an expression is considered “simplified” or not.
Things like x^2 - 1 are not considered simplified because they are not factorised, but things like (x + 3)^2 + 2 (x - 4) + 7 are also not considered simplified.
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