Square of Sum Calculator
Expand binomials of degree 2 instantly. Visualizes the step-by-step expansion of (a + b)² with clear coefficient multiplication for algebra students.
About
Algebra students often stumble when expanding binomials, specifically forgetting the middle term in the expansion process. Accuracy is critical here because a single sign error or missing coefficient propagates through subsequent calculus or physics problems. This tool isolates the mechanics of the perfect square trinomial pattern. It breaks down the multiplication of coefficients and variables, ensuring that the cross-product term is calculated and displayed correctly. It is designed for students verifying homework or engineers needing a quick check on polynomial arithmetic.
Formulas
The fundamental expansion for the square of a sum is derived from the distributive property of multiplication over addition.
When terms include coefficients, such as (Ax + B)2, the middle term becomes:
Reference Data
| Expression type | Expansion Pattern | Common Mistake |
|---|---|---|
| Basic Sum | a2 + 2ab + b2 | Missing 2ab |
| Difference | a2 − 2ab + b2 | Sign errors |
| Coefficients | (2x + 3)24x2 + 12x + 9 | Squaring sum separately |
| Variables | (x + y)2 | x2 + y2 (False) |
| Complex | (3x + 4y)2 | Calculation speed |
| Radicals | (√x + 1)2 | Simplifying roots |
| Imaginary | (a + bi)2 | i2 definition |
| Functions | (sin(x) + cos(x))2 | Trig identities |