Number and algebraAdditional / Further Maths

Positive-integer binomial expansion

Use binomial coefficients to expand a bracket with a positive integer power.

  • For a positive integer , the expansion of ends after terms.
  • Use the coefficients .
  • The power of decreases as the power of increases. Keep negative terms in brackets.

Example 1

Expand and simplify.

Use the binomial coefficients.
Use the binomial coefficients.

Example 2

Expand and simplify.

Use the binomial coefficients.
Use the binomial coefficients.

Remember
.

Your turn

Question 1

Expand and simplify.

Check answer
Use the binomial coefficients.
Use the binomial coefficients.
Question 2

Expand and simplify.

Check answer
Use the binomial coefficients.
Use the binomial coefficients.
Question 3

Expand and simplify.

Check answer
Use the binomial coefficients.
Use the binomial coefficients.
Question 4

Expand and simplify.

Check answer
Use the binomial coefficients.
Use the binomial coefficients.
Question 5

Expand and simplify.

Check answer
Use the binomial coefficients.
Use the binomial coefficients.
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