Below an example is explained.

Determine whether the expression 6

^{2x}- 2

^{2x}can be divided by 4.

You can solve this maths challenge through various approaches.

One approach is to substitute the variable "x" in the expression by an ambiguous integer. The number obtained, after the substitution, can be easily determined by applying the divisibility by 4 rule. Click on

**this link**to view the divisibility by 4 rule.

However, this approach is mathematically not elegant. It suffices, though, to meet the question objective.

A better approach that looks more mathematically professional, is the application of factorisation to determine the possibility of divisibility by 4.

This approach requires prior knowledge of the factorisation method to the given maths problem.

**Factorisation method**to the general expression a

^{k}- b

^{k }:

a

^{k}- b

^{k}= (a - b)(a

^{k-1}+ a

^{k-2}b + ... + ab

^{k-2}+ b

^{k-1})

Therefore by re-writing 6

^{2x}- 2

^{2x}=

**(6 - 2)**( ........), it becomes very obvious that the given challenge can be divide by 4 since the first written factor of the expression is

**(6 - 2)**= 4!

The message here is that there are various ways to achieve the objective of the maths question. It is a matter of which method is creative or interesting and involves mathematically challenging steps. The approach can be direct and less conceptual or conceptually involved with application of maths theorems. Both are, within their own definition, creative in nature.

A new mindset looking at maths as it is, can change this exciting subject to a life-aspiring adventure with challenges that buils up a person's character.

Wonderful maths .....

:-)

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