Formulas of algebraic expression?

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Formulas of Algebraic Expressions

Algebraic expressions are mathematical expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions are used to represent relationships between quantities and are an essential part of algebra.

There are several formulas that are commonly used in algebraic expressions to solve various mathematical problems. These formulas help in simplifying expressions, solving equations, and finding the values of variables. Some of the important formulas of algebraic expressions include:

1. Distributive Property:
The distributive property states that a(b + c) = ab + ac. This property allows the multiplication of a number or variable to be distributed to each term inside the parentheses.

2. Commutative Property:
The commutative property states that a + b = b + a and ab = ba. This property allows the rearrangement of terms in an expression without changing the result.

3. Associative Property:
The associative property states that (a + b) + c = a + (b + c) and (ab)c = a(bc). This property allows the grouping of terms in an expression without changing the result.

4. Identity Property:
The identity property states that a + 0 = a and a × 1 = a. This property states that adding zero to a number or multiplying a number by one does not change its value.

5. Inverse Property:
The inverse property states that a + (-a) = 0 and a × (1/a) = 1. This property states that adding the additive inverse of a number to the number gives zero, and multiplying a number by its multiplicative inverse gives one.

6. Quadratic Formula:
The quadratic formula is used to find the roots of a quadratic equation. The formula is given by x = (-b ± √(b^2 - 4ac))/(2a), where a, b, and c are coefficients of the quadratic equation.

7. Pythagorean Theorem:
The Pythagorean theorem is used to find the length of the hypotenuse or one of the sides of a right triangle. The formula is given by a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

8. Formula for the area of a rectangle:
The formula for the area of a rectangle is given by A = l × w, where A is the area, l is the length, and w is the width of the rectangle.

9. Formula for the area of a circle:
The formula for the area of a circle is given by A = πr^2, where A is the area, π is a constant approximately equal to 3.14159, and r is the radius of the circle.

These are just a few of the many formulas used in algebraic expressions. Understanding and applying these formulas can help in solving a wide range of mathematical problems and equations.

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