Term Independent of X Calculator
Verified Calculation Engine
The online Term Independent of X Calculator helps you calculate instantly and solve problems related to Binomial Theorem. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Finds the term independent of x (constant term) in binomial expansion of (ax^p + bx^q)^n.
For (ax^p + bx^q)^n, term independent of x occurs when:
p(n-r) + qr = 0
Solve for r, then T(r+1) = nCr a^(n-r) b^r
Constant term has power of x equal to zero
Inputs
Results
Worked Examples
Example 1: Basic
Find term independent of x in (x + 1/x)^4
- a: 1
- p: 1
- b: 1
- q: -1
- n: 4
- term: 6
- r: 2
- termNumber: 3
Example 2: Board Level
Find term independent of x in (x² + 1/x)^6
- a: 1
- p: 2
- b: 1
- q: -1
- n: 6
- term: 15
- r: 4
- termNumber: 5
About this calculator
Overview
Term Independent of X Calculator evaluates Term Independent of X for the math / binomial-theorem library. Primary input cue: Coefficient a [required]: Coefficient of first term. Method anchor: For (ax^p + bx^q)^n, term independent of x occurs when: p(n-r) + qr = 0 Solve for r, then T(r+1) = nCr a^(n-r) b^r. Constant term has power of x equal to zero.
When to use
Reach for Term Independent of X Calculator to compare scenarios by changing one input at a time for term independent of x.
Inputs explained
- Coefficient a [required]: Coefficient of first term
- Power of x in First Term [required]: Power p
- Coefficient b [required]: Coefficient of second term
- Power of x in Second Term [required]: Power q
- Power n [required]: Power
Formula / method
For (ax^p + bx^q)^n, term independent of x occurs when: p(n-r) + qr = 0 Solve for r, then T(r+1) = nCr a^(n-r) b^r. Constant term has power of x equal to zero (calculator id: term-independent-of-x-calculator).
Worked example
Worked values: a = 1, p = 1, b = 1, q = -1, n = 4 → term = 6, r = 2, termNumber = 3
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for term independent of x.
Assumptions
- Units (when shown) must be consistent across inputs for term independent of x. [term-independent-of-x-calculator]
- Empty required inputs are not silently replaced with zeros for term independent of x.
- Real-number arithmetic is used unless term independent of x explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to term independent of x.
- Term Independent of X Calculator cannot invent missing inputs; incomplete forms stop short of a forged term independent of x value.
- Complex/branch cuts and undefined points are not always interactively annotated for term independent of x.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
For (ax^p + bx^q)^n, term independent of x occurs when: p(n-r) + qr = 0 Solve for r, then T(r+1) = nCr a^(n-r) b^r. Constant term has power of x equal to zero (calculator id: term-independent-of-x-calculator).
Example Calculation
Worked values: a = 1, p = 1, b = 1, q = -1, n = 4 → term = 6, r = 2, termNumber = 3
Frequently Asked Questions
What is Term Independent of X Calculator?
- Term Independent of X Calculator evaluates Term Independent of X for the math / binomial-theorem library. Primary input cue: Coefficient a [required]: Coefficient of first term. Method anchor: For (ax^p + bx^q)^n, term independent of x occurs when: p(n-r) + qr = 0 Solve for r, then T(r+1) = nCr a^(n-r) b^r. Constant term has power of x equal to zero.
How does Term Independent of X Calculator work?
- For (ax^p + bx^q)^n, term independent of x occurs when: p(n-r) + qr = 0 Solve for r, then T(r+1) = nCr a^(n-r) b^r. Constant term has power of x equal to zero (calculator id: term-independent-of-x-calculator).
Why use this Math Numbers calculator?
- Reach for Term Independent of X Calculator to compare scenarios by changing one input at a time for term independent of x.