Square of Binomial Calculator

Calculate (a+b)² and (a-b)² using algebraic formulas

Operation Type

Value of a

Value of b

📐Binomial Square Formulas

Square of Sum

(a + b)² = a² + 2ab + b²

First squared + twice product + second squared

Square of Difference

(a - b)² = a² - 2ab + b²

First squared - twice product + second squared

⚠Common Mistakes to Avoid

Wrong: (a + b)² = a² + b²

Missing the middle term!

You must include 2ab

Correct: (a + b)² = a² + 2ab + b²

Don't forget the 2ab term

All three terms needed

💡Worked Examples

(3 + 4)²

= 3² + 2(3)(4) + 4²

= 9 + 24 + 16

= 49

(5 - 2)²

= 5² - 2(5)(2) + 2²

= 25 - 20 + 4

= 9

(x + 5)²

= x² + 2(x)(5) + 5²

= x² + 10x + 25

(2x - 3)²

= (2x)² - 2(2x)(3) + 3²

= 4x² - 12x + 9

💼Applications

Algebra

• Expanding expressions

• Factoring

• Simplification

Geometry

• Area calculations

• Square dimensions

• Pythagorean theorem

Number Theory

• Mental math tricks

• Quick calculations

• Pattern recognition