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Mathematics has been utilized in civilizations like Egypt and Babylonia for practical purposes, such as building structures and calculating land area for community growth. Greek thinkers, who studied geometry and numbers, contributed to its growth into a field of concepts. Mathematics has driven technical developments and laid the groundwork for current science as cultures evolved. Its contributions have been instrumental in understanding our surroundings and preserving resources.


In order to standardize algebraic formulas and make them more standardized and logical, Robert Recorde created early notation. Later mathematicians were able to develop more complex mathematical theories and more effectively address real-world issues thanks to this notation, symbols, and the equals sign.

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The foundational principles of mathematics—addition, subtraction, multiplication, division, exponents, and geometry—serve as core tools for understanding quantity and space. Addition combines values to increase amounts, while subtraction does the opposite, removing quantity to find what remains. Multiplication extends addition by scaling a number through repeated addition, and division breaks a quantity into equal parts, reversing multiplication. Exponents take multiplication further by raising a number to a power, representing repeated multiplication (e.g., 3^2 means 3 \times 3). Geometry, meanwhile, explores shapes, sizes, and spatial properties, enabling us to measure and understand spatial relationships. Together, these principles allow us to solve practical problems, build complex math concepts, and apply mathematical thinking to the world around us.

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Basic Math Formulas

Operation Formula Example
Addition a + b 5 + 3 = 8
Subtraction a - b 10 - 4 = 6
Multiplication a × b 6 × 3 = 18
Division a / b 12 / 4 = 3
Exponent an 23 = 8
Area of Circle πr2 π × 32 ≈ 28.27
Perimeter of Square 4a 4 × 5 = 20
Pythagorean Theorem a2 + b2 = c2 32 + 42 = 52
Slope of Line (y₂ - y₁) / (x₂ - x₁) (6 - 2) / (3 - 1) = 2

Expansion Questions and Answers

Question 1: Expand (x + 3)(x + 5) Question 2: Expand (2x - 4)(x + 6)

Step-by-Step Answer:

1. Apply the distributive property: (x + 3)(x + 5) = x(x + 5) + 3(x + 5)

2. Expand each term: x(x + 5) = x2 + 5x, and 3(x + 5) = 3x + 15

3. Combine like terms: x2 + 5x + 3x + 15

4. Simplify: x2 + 8x + 15

Step-by-Step Answer:

1. Apply the distributive property: (2x - 4)(x + 6) = 2x(x + 6) - 4(x + 6)

2. Expand each term: 2x(x + 6) = 2x2 + 12x, and -4(x + 6) = -4x - 24

3. Combine like terms: 2x2 + 12x - 4x - 24

4. Simplify: 2x2 + 8x - 24