Mathematics

Algebra and Geometry

# Algebraic expressions and equations

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Algebraic expressions and equations

Algebraic Expressions

- An
**algebraic expression**is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide). **Variables**are symbols used to represent unknown numbers or values. They are typically represented by letters, such as x, y, or z.- The
**terms**of an algebraic expression are the parts of the expression that are added or subtracted. Each term can be a number, a variable, or a product or quotient of numbers and variables. - Algebraic expressions can be
**simplified**by combining like terms, which are terms with exactly the same variables and powers. - The
**coefficient**is the numerical factor in any term. For example, in 5x, the coefficient is 5. - To
**evaluate**an algebraic expression, you replace the variable with a given number and then perform the operations in the expression.

Algebraic Equations

- An
**algebraic equation**is a statement of equality between two algebraic expressions. - The
**solution**of an algebraic equation is the numerical value of the variable that makes the equation true. - An algebraic equation can be
**solved**by isolating the variable, which often involves addition, subtraction, multiplication, or division. - Sometimes, you'll need to use the distributive property to remove parentheses before isolating the variable.
**Quadratic equations**are algebraic equations that have a degree of 2. Their solutions can be found using factoring, completing the square, or using the quadratic formula.**System of equations**is a set of two or more equations that all contain the same set of variables. Systems can be solved by graphing, substitution, or elimination.- A
**linear equation**forms a straight line when graphed. It has no exponents higher than 1, and its graph is a straight line. You can solve a linear equation by isolating the variable.

Algebraic Formulae

- A
**formula**is a type of equation that shows the relationship between different variables. - An
**algebraic formula**can be used to calculate measurements, like the area of a circle or rectangle, or the volume of a cylinder or sphere. - The formula for a
**linear sequence**is an + b, where a is the common difference and b is the first term. - The formula for a quadratic sequence is an^2+ bn + c, where a, b and c are constants.
- The formula for the
**sum of an arithmetic series**is Sn = n/2 * (a + l), where Sn is the sum of the first n terms, a is the first term, l is the last term, and n is the number of terms.