Basic Math Formulas of Algebra

Master Algebra with our guide to basic math formulas. Learn quadratic equations, binomial expansions, and exponent laws to boost your math skills.

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The Foundation of Logical Reasoning

Algebra is often called the “language of logic.” Unlike basic arithmetic, algebra introduces variables—letters like $x$ and $y$ that represent unknown numbers. Whether you are a student or a data analyst, these formulas are the building blocks of modern problem-solving.

1. Basic Expansion Formulas

These are the “identities” that every student must memorize. They help in simplifying complex expressions instantly.

Square of a Sum: $(a + b)^2 = a^2 + 2ab + b^2$
Square of a Difference: $(a - b)^2 = a^2 - 2ab + b^2$
Difference of Squares: $a^2 - b^2 = (a - b)(a + b)$
Cube of a Sum: $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

2. Solving Quadratic Equations

A quadratic equation is any equation that can be rearranged in the form $ax^2 + bx + c = 0$ . To find the value of $x$ , we use the Quadratic Formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

The term $b^2 - 4ac$ is called the discriminant. It tells us if the roots are real or imaginary.

3. Laws of Exponents

Exponents (powers) are frequent in algebra. Understanding how to manipulate them is vital:

Product Rule: $a^m \cdot a^n = a^{m+n}$
Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$
Power of a Power: $(a^m)^n = a^{m \cdot n}$