Algebraic formulas

Here are some commonly used algebraic formulas:

Quadratic formula: If you have a quadratic equation of the form ax^2 + bx + c = 0, then the solution for x can be found using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Distance formula: The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Pythagorean theorem: In a right triangle with legs of length a and b, and hypotenuse of length c, the Pythagorean theorem states that:

a^2 + b^2 = c^2

Slope-intercept form of a linear equation: The equation of a line with slope m and y-intercept b is given by:

y = mx + b

Point-slope form of a linear equation: The equation of a line passing through the point (x1, y1) with slope m is given by:

y - y1 = m(x - x1)

Sum and difference of cubes: The formulas for the sum and difference of two cubes are:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

These are just a few examples of algebraic formulas, but there are many more!

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