Free GCSE Expanding binomials practice questions with full step-by-step worked solutions. Covers expanding double brackets, FOIL, squaring a binomial, perfect square. Practise exam-style problems and check your method.
Set up the expansion (FOIL)
Every term in the first bracket must be multiplied by every term in the second.
Multiply out the pairs
Multiply the First, Outer, Inner and Last terms to get four terms.
Collect like terms
Combine the x-terms and to get .
Set up the expansion (FOIL)
Every term in the first bracket must be multiplied by every term in the second.
Multiply out the pairs
Multiply the First, Outer, Inner and Last terms to get four terms.
Collect like terms
Combine the x-terms and to get .
Set up the expansion (FOIL)
Every term in the first bracket must be multiplied by every term in the second.
First and Outer terms
Multiply the first terms in each bracket, then the outer terms.
Inner and Last terms
Multiply the inner terms, then the last terms — watch the signs.
Write out the four terms
Bring the four products together before simplifying.
Collect like terms
Combine the x-terms and -x to get .
State the expansion
This is the expansion written in standard form.
Set up the expansion (FOIL)
Every term in the first bracket must be multiplied by every term in the second.
First terms
Multiply the first term of each bracket.
Outer terms
Multiply the two outer terms.
Inner terms
Multiply the two inner terms.
Last terms
Multiply the last term of each bracket.
Write out all four terms
List every product from FOIL.
Collect like terms
Combine the x-terms and to get .
Identify the leading term
The highest power is x squared with coefficient 6.
Check by substituting
The original product and the expansion both give when , so the working checks out.
State the final answer
The expansion in expanded and simplified form.
Plan the expansion
Expand two of the brackets first, then multiply the result by the third.
Multiply the first two brackets
Use FOIL on the first pair of brackets.
Simplify the quadratic
Combine the x-terms and to get .
Set up the next multiplication
Now multiply this quadratic by the remaining bracket (x - 1).
Multiply the x-squared term
Distribute the x-squared term across the bracket.
Multiply the x term
Distribute the middle term of the quadratic over the bracket.
Multiply the constant term
Distribute the constant term across the bracket.
Write out all six terms
Collect every product before simplifying.
Group the x-cubed term
There is only one x-cubed term: .
Group the x-squared terms
Add the two x-squared terms together.
Group the x terms
Add the two x terms together.
Group the constant term
The only constant term is .
Write the expansion in standard form
Arrange the terms from the highest power of x to the lowest.
Check by substituting
Both the original product and the expansion give when .
State the final answer
This is the fully expanded and simplified expression.
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