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Instant Calculation
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Squaring a binomial always follows the same predictable pattern — (a+b)²=a²+2ab+b² — so once you recognize it, there's no need to FOIL it out term by term. This tool applies that pattern directly and shows each piece.
How it works
With a=mx and b=n, the three terms of the pattern are computed directly: a²=(mx)² for the leading term, 2ab=2(mx)(n) for the middle term (with its sign matching whether it's a sum or difference), and b²=n² for the constant.
- Enter m (coefficient of x).
- Enter sign.
- Enter n (constant).
- Click Calculate to see your results.
Examples
A sum squared
(3x+5)² = 9x²+30x+25.
A difference squared
(2x-1)² = 4x²-4x+1.
Who should use it
- Algebra coursework introducing the perfect-square binomial pattern.
- A quick shortcut before completing the square, which relies on this exact pattern.
Industry applications
- Mathematics education
Advantages
- Shows each of the three pattern terms individually before combining.
- Handles both the sum and difference cases.
Limitations
- Limited specifically to squaring a binomial — for cubes or other powers, different patterns apply.
Common mistakes to avoid
- A very common algebra error: writing (a+b)² = a²+b², forgetting the middle 2ab term entirely.
Best practices
- Whenever you see a binomial squared, reach for this pattern directly instead of FOILing it out — it's faster and less error-prone.
Tips
- This exact pattern, run in reverse, is also what the Perfect Square Trinomial calculator checks for — recognizing a²+2ab+b² lets you skip straight to the squared binomial form.