Young Geniuses · Ages 13 to 14

Binomial Expansion MCQ

Expand binomials using the binomial theorem, choosing from four options. A Grade 8–9 algebra worksheet with answer keys.

Multiple Choice WorksheetGrades binomial, expansion, multiple-choice5 difficulty levels8 questions

The learning journey

Every activity is one step. Here is where this one fits.

  1. PlayLearn the idea in a game
  2. Practise(you are here)Lock it in on paper
  3. ReviewCome back and keep it sharp
  4. MasterTake on a harder challenge
  5. AchieveEarn a certificate

About Binomial Expansion MCQ

Binomial Expansion MCQ gives ambitious upper-secondary learners practice expanding binomials using the binomial theorem and its coefficients. Each question asks the student to identify a coefficient in the expansion of a binomial raised to a power, choosing the correct value from four options. The binomial theorem, and the pattern of coefficients found in Pascal’s triangle, is an enrichment and early high-school topic across the US, UK, Canada and Australia, and it provides a powerful shortcut for expanding expressions that would otherwise be tedious to multiply out. Understanding where each coefficient comes from — combining the binomial coefficient with the powers of each term — builds both algebraic fluency and an appreciation of the elegant structure behind the expansion. The multiple-choice format suits the topic because the distractors are built around common errors, such as forgetting the coefficient or mishandling the power, helping students notice and correct them. The binomials vary so the worksheet stays fresh and reusable, and the five levels increase the size of the terms. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving the correct option and value. There is no advertising and no sign-up.

Common questions

What is the binomial theorem?
A rule for expanding (a + b)ⁿ using the coefficients from Pascal’s triangle.
What grade is this for?
Grade 8 to Grade 9 learners aged 13 to 14, as an enrichment topic.
Is an answer key included?
Yes, every level gives the correct option and value.

A hand for grown-ups

Before you start
Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
While they work
Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
Afterwards
Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
Watch out for
Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
Away from the screen
Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.

Chosen by the skills this activity practises.