Algebraic equations for multiplying binomials
In algebra, multiplying binomials is easier if you recognize their patterns. You multiply the sum and difference of binomials and multiply by squaring and cubing to find some of the special products in algebra. See if you can spot the patterns in these equations:
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Sum and difference: (a + b)(a – b) = a2 – b2
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Binomial squared: (a + b)2 = a2 + 2ab + b2
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Binomial cubed: (a + b)3 = a3 + 3a2b + 3ab2 + b3
Algebra's quadratic formula
You can find solutions for quadratic equations by factoring, completing the square, guessing, or everyone’s favorite — using the quadratic formula. The best thing about the quadratic formula (unlike the other methods) is that it always works.
Rules for algebraic radicals
Working with radicals can be troublesome, but these equivalences keep algebraic radicals from running amok. Finding the root of product or quotient or a fractional exponent is simple with these formulas; just be sure that the numbers replacing the factors a and b are positive.
Algebra’s laws of logarithms
Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1.
Standard equations of algebraic conics
Conics are curved algebraic forms that come from slicing a cone with a plane. Use these equations to graph algebraic conics, such as circles, ellipses, parabolas, and hyperbolas:
Cramer's rule for linear algebra
Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix.
Using algebra to find the sums of sequences
Algebra can help you add a series of numbers (the sum of sequences) more quickly than you would be able to with straight addition. Adding integers, squares, cubes, and terms in an arithmetic or geometric sequence is simple with these algebraic formulas:
Algebraic Permutations and Combinations
In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn’t matter. The formulas you need are
Eight basic algebraic curves
Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here’s a look at eight of the most frequently used graphs.
