Square of a Binomial Calculator

Expand (ax + b)² into a perfect-square trinomial.

x² coefficient 1

x coefficient 10

constant 25

Formula: (ax + b)² = a²·x² + 2ab·x + b²

Step-by-step with your numbers:

1. Values used:

2. a = 1

3. b = 5

5. x² coefficient = 1

6. x coefficient = 10

7. constant = 25

Did we solve your problem today?

Squaring a binomial produces a perfect-square trinomial with a fixed pattern.

The math behind it

(ax + b)² = a²x² + 2ab x + b². The middle term is twice the product of the two terms — a common source of mistakes when people forget it.

(x + 5)² = x² + 10x + 25.

Is (a + b)² equal to a² + b²?

No. You must include the cross term: (a + b)² = a² + 2ab + b².