AI generatedAlgebraKey Stage 3

Proving two expressions are equivalent

Transform both sides or simplify their difference.

  • State that the variable represents an integer when proving integer properties.
  • Use algebra to cover every permitted value. Factor out the divisor or 2 when helpful.
  • One counterexample disproves a universal statement; several examples do not prove it.

Example 1

Show these expressions are equivalent.

Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .

Example 2

Show these expressions are equivalent.

Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .

Your turn

Question 1

Show these expressions are equivalent.

Check answer
Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .
Question 2

Show these expressions are equivalent.

Check answer
Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .
Question 3

Show these expressions are equivalent.

Check answer
Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .
Question 4

Show these expressions are equivalent.

Check answer
Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .
Question 5

Show these expressions are equivalent.

Check answer
Expand the bracket.Collect the terms. The result matches the second expression for every .
The expressions are equivalent for all .
← All Algebra cardsReport a mistake