How this calculator works
Squaring a binomial means multiplying it by itself. The two cross products are equal, so they combine into 2abx. Both outer squared terms are non-negative for real inputs; the middle sign depends on ab. If a is zero the result is a constant, and if b is zero it is a single squared term. Recovery modes take both square-root signs, since a square does not determine the original sign.
Formula
(ax + b)^2 = a^2*x^2 + 2ab*x + b^2.
Worked example
(2x - 3)^2 = 4x^2 - 12x + 9. The middle term is 2 x 2 x (-3)x = -12x. For (x + 5)^2, the result is x^2 + 10x + 25.
Advertisement
Frequently asked questions
Why is a^2 + b^2 not enough?
The two cross products do not disappear. They contribute the middle term 2abx.
How do I enter subtraction?
Choose Minus with b = 3, or choose Plus with b = -3. Selecting Minus with a negative b produces addition.
Can a be negative?
Yes. For example, (-x + 2)^2 equals x^2 - 4x + 4.