Pascal coefficients and finite binomial expansion · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Finite binomial expansions — objective 1

Maths4U Original · Short practice

Consider \(\left(5 x + 2\right)^{7}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Finite binomial expansions — objective 1

Maths4U Original · Short practice

Consider \(\left(2 x + 3\right)^{4}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Finite binomial expansions — objective 2

Maths4U Original · Short practice

Consider \(\left(2 x + 3\right)^{4}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Finite binomial expansions — objective 2

Maths4U Original · Short practice

Consider \(\left(3 x + 1\right)^{5}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Finite binomial expansions — objective 3

Maths4U Original · Short practice

Consider \(\left(3 x + 1\right)^{5}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^2\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Finite binomial expansions — objective 3

Maths4U Original · Short practice

Consider \(\left(4 x + 2\right)^{6}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^2\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Finite binomial expansions — objective 4

Maths4U Original · Short practice

Consider \(\left(4 x + 2\right)^{6}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^3\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Finite binomial expansions — objective 4

Maths4U Original · Short practice

Consider \(\left(5 x + 3\right)^{7}\). Work without a calculator.

Find the coefficient of \(\displaystyle x^3\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →