Square of a Binomial Calculator
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Square of a Binomial Formulas
The square of a binomial can be calculated using these formulas:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Where:
- a² is the square of the first term
- 2ab is twice the product of both terms
- b² is the square of the second term
Geometric Interpretation
The square of a binomial can be visualized as the area of a square:
For (a + b)²:
- Total area = (a + b) × (a + b)
- Can be split into:
- a² (square of first term)
- 2ab (two rectangles)
- b² (square of second term)
For (a - b)²:
- Total area = (a - b) × (a - b)
- Can be split into:
- a² (square of first term)
- -2ab (two rectangles)
- b² (square of second term)
Example Problems
Example 1: (x + 3)²
Step 1: Identify a and b
- a = x
- b = 3
Step 2: Apply the formula
(x + 3)² = x² + 2(x)(3) + 3²
Step 3: Simplify
= x² + 6x + 9
Example 2: (2x - 5)²
Step 1: Identify a and b
- a = 2x
- b = 5
Step 2: Apply the formula
(2x - 5)² = (2x)² - 2(2x)(5) + 5²
Step 3: Simplify
= 4x² - 20x + 25
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