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Elementary algebra

algebra history

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The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.

Slope-intercept Form

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Common exercises will give you some pieces of information about a line, and you will have to come up with the equation of the line. How do you do that? You plug in whatever they give you, and solve for whatever you need, like this: Find the equation of the straight line that has slope m = 4 and passes through the point (?1, ?6). Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = ?1 and y = ?6.

Quadratic Formula

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Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients". The Formula is derived from the process of completing the square, and is formally stated as: For ax2 + bx + c = 0, the value of x is given by:

Algebra Formulas

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Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn a0 = 1 (am)/(an) = am-n a-m= 1/(am) Quadratic Formula In an equation like ax2 + bx + c = 0 You can solve for x using the Quadratic Formula: Binomial Theorem (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on... Difference of Squares a2 - b2 = (a - b)(a + b) Rules of Zero 0/x = 0 where x is not equal to 0. a0 = 1 0a = 0 a*0 = 0 a/0 is undefined (you can't do it)

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