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Prove algebraically that (4n + 1)² − (2n − 1) is an even number for all positive integer values of n.

First of all expand the brackets and simplify the expression given:(4n+1)(4n+1)-(2n-1)= 8n 2 +8n+1-2n+1= 8n 2 +6n+2= 2(4n 2 +3n+1). Since the expression can be factorised with 2, and since 4n 2 +3n+1 will al...
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Answered by Shiv M. • Maths tutor
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dux Gallorum timebat ne Romani viros collem ascendentes audirent. itaque imperavit omnibus Gallis ut in itinere tacerent. ea nocte Galli tam tacite processerunt ut custodes Romani eos non conspicerent.

The leader of the Gauls was afraid that the Romans might hear the men climbing the hill.And so he ordered all the Gauls to say nothing on the journey.That night the Gauls advanced so silently that the Roman ...
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Answered by Kishan M. • Latin tutor
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How to recognise and make the link between probability and the algebraic demands of this question?

While I doubt students will ask this exact question, think it provides the basis for what are usually the most difficult questions in GCSE papers, and students would usually be unsure where to start. My insp...
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Answered by Neeraj K. • Maths tutor
3417 Views

In a circuit with a 12V battery, 20Ω resistor and 10Ω resistor, all in series, calculate the current that would flow?

This question can be split into two parts, the first is calculating overall resistance: in series the R total = R 1 + R 2 so here R total = 10Ω + 20Ω = 30Ω The second is to choose the relevant equation, pote...
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Answered by Lauren A. • Biology tutor
5573 Views

How do I remeber the specific elements of a treaty?

I find it easiest to remember the different elements of a treaty by creating an acronomyn. For example, the Treaty of Versailles angered many germans due to four clauses. Loss of territories, limitations on ...
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Answered by Lucinda M. • History tutor
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