Proving Algebraic Identities

This lesson covers:

  1. How to prove that algebraic identities are true
  2. We do this by rearranging one side of the identity (e.g. the left) to look like the other side (e.g. the right)
  3. E.g. 'Prove algebraically that (n + 4)2 - n(n + 2) ≡ 2(3n + 8)'

When proving algebraic identities you must rearrange one side of the identity to make it look like the other side.


The marks for these questions come entirely from your working steps. As there are multiple ways of doing the workings, we can't mark them automatically. Instead we'll show you the simplest set of steps in the hints, and trust you to say whether you managed to rearrange it correctly or not. 

Prove that the identity below is true.

(x+4)2≡ x2+ 8x+16

I got it correct

I got it wrong

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1

Prove that the identity below is true.

(x+7)2≡ x2+14x+49

I got it wrong

I got it correct

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1

Prove that the identity below is true.

2(x+4)2−4(4x+5)≡2(x2+6)

I got it correct

I got it wrong

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1

Prove that the identity below is true.

3(x+4)2+ x(x−24)−20≡4(x2+7)

I got it correct

I got it wrong

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1

Prove that the identity below is true.

2(x+5)2−20(x+2)≡2(x2+5)

I got it correct

I got it wrong

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1

Prove that the identity below is true.

2(x − 3)2+3(4x + 2)−14≡2(x2+5)

I got it correct

I got it wrong

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1

Prove that the identity below is true.

2(x+3)2−3(4x−5)−9≡2(x2+12)

I got it wrong

I got it correct

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1

Prove that the identity below is true.

3(x+2)2−12(x+3)+33≡3(x2+3)

I got it wrong

I got it correct

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1

Prove that the identity below is true.

2(x + 6)2−50≡2(x + 11)(x + 1)

I got it correct

I got it wrong

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1