The general term and powers of x: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^3\) in \((1+x)^7\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: check 2
Difficulty: ★★☆Maths4U Original · Short practice
In \((2+x)^5\), find the coefficient of \(x^4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Find the constant term in \((x^2+2/x)^3\), \(x\ne0\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: check 4
Difficulty: ★★☆Maths4U Original · Short practice
For a non-negative integer \(n\), which expression is the term containing \(x^r\) in \((a+bx)^n\), where \(r\) is an integer and \(0\le r\le n\)?Choose one answer.
Coefficients in products and parity: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^2\) in \((1+x)(1+2x)^3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x\) in \((2-x)(1+3x)^2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^3\) in \((1-x)(1+x)^4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: check 4
Difficulty: ★★☆Maths4U Original · Short practice
When multiplying two polynomials in non-negative powers of \(x\), which pairs of exponents contribute to the coefficient of \(x^2\)?Choose one answer.
The general term and powers of x: check 5
Difficulty: ★★☆Maths4U Original · Short practice
Evaluate \(\frac{6!}{2!4!}\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^3\) in \((1+x)^8\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^4\) in \((3+x)^5\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Find the constant term in \((x+3/x)^4\), x nonzero.Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^2\) in \((2+5x)^3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
The general term and powers of x: review variant 5
Difficulty: ★★☆Maths4U Original · Short practice
Evaluate \(8!/(2!6!)\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^2\) in \((1+2x)(1+3x)^2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of x in \((4-x)(1+2x)^2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^3\) in \((1-2x)(1+x)^4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Coefficients in products and parity: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Find the coefficient of \(x^2\) in \((1+x+x^2)(1+2x+3x^2)\).Enter one number or fraction. Round decimals to at least six decimal places when needed.