Square of a Binomial Calculator
Expand binomial squares (a+b)² and (a-b)² with step-by-step solutions
Calculate Square of Binomial
Binomial Expansion Results
Formulas Used
Example Calculation
Simple Example: (6 - b)²
Given: a = 6, form = (a - b)²
Step 1: (6 - b)²
Step 2: 6² - (2 × 6 × b) + b²
Result: 36 - 12b + b²
Advanced Example: (17x + 210)²
Given: a = 17, b = 210
Step 1: (17x + 210)²
Step 2: (17x)² + 2(17x)(210) + 210²
Result: 289x² + 7,140x + 44,100
Binomial Square Formulas
(a + b)²
= a² + 2ab + b²
Sum of squares
(a - b)²
= a² - 2ab + b²
Difference of squares
Perfect Square Trinomial
Result of binomial²
Three-term polynomial
Quick Tips
The middle term is always 2ab
Perfect square trinomials factor back to binomials
Sign of middle term depends on binomial sign
First and last terms are always positive
Understanding Square of a Binomial
What is a Binomial Square?
The square of a binomial is the result of multiplying a binomial expression by itself. When you square a binomial like (a + b), you get a perfect square trinomial with three terms.
Perfect Square Trinomial
- •First term: square of first term in binomial (a²)
- •Middle term: twice the product of both terms (±2ab)
- •Last term: square of second term in binomial (b²)
How to Expand
(a ± b)² = a² ± 2ab + b²
Step 1: Square the first term
Step 2: Multiply first and second terms, then double
Step 3: Square the second term
Step 4: Combine with appropriate signs
Remember: The sign of the middle term matches the binomial's sign.
Common Applications
Algebra
Expanding expressions and solving equations
Geometry
Calculating areas of squares with variable sides
Physics
Modeling quadratic relationships