Proving two expressions are equivalent Revision Card

AI generatedAlgebraKS3 / GCSE

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