Square of a Binomial Calculator

A binomial is an algebraic expression containing two terms joined by addition or subtraction. Squaring a binomial means multiplying the entire expression by itself, not simply squaring each term. The square of a binomial calculator expands the expression into three terms and also evaluates it when numerical values are supplied. It handles both a plus b squared and a minus b squared, making it useful for algebra practice, mental arithmetic, polynomial expansion, and checking intermediate work. For a sum, distributive multiplication gives a squared plus ab plus ab plus b squared. Combining the two identical middle products produces the identity a squared plus 2ab plus b squared. For a difference, the cross-products are both negative, producing a squared minus 2ab plus b squared. Notice that the last term remains positive because a negative quantity multiplied by itself is positive. Forgetting the doubled middle term or assigning a negative sign to the last term are the two most common errors. Suppose a is 3 and b is 4. The square of their sum expands into 9 plus 24 plus 16, which totals 49. This agrees with directly squaring 7. If a is 10 and b is 3 and subtraction is selected, the expansion becomes 100 minus 60 plus 9, which totals 49. This agrees with directly squaring 7 as well. Comparing the expanded result with the direct calculation is a quick way to verify the identity. The identities work for positive numbers, negative numbers, decimals, variables, and more complicated expressions. In this calculator, a and b are numerical so each coefficient and the final value can be displayed clearly. A negative input is treated as the full term value. For example, entering negative 2 for b in addition mode is mathematically equivalent to subtracting 2. Choose the operation that best represents the original written expression to keep the explanation easy to follow. Binomial squares appear in quadratic equations, completing the square, geometry, probability, and approximation methods. Geometrically, a plus b squared can be viewed as the area of a large square split into one a-by-a square, two a-by-b rectangles, and one b-by-b square. That visual model explains exactly why the middle product occurs twice. Use the calculator to confirm arithmetic, but retain the identity so you can recognize and factor perfect-square trinomials in reverse.