What Are Some Basic Algebra Formulas?


Quick Answer

One of the most commonly used algebra formulas is the quadratic formula. The quadratic formula, x={[-b+-sqrt(b^2-4ac)]/2a}, is used to solve the roots, or values of x, in a quadratic equation, such as a(x^2)+bx+c, wherein a, b, and c are numerical coefficients.

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Full Answer

Usually, to arrive at the answer for a quadratic equation, mathematicians factor the quadratic, then equate each factor to zero, and solve for x. However, not all equations are factorable. Hence, the quadratic formula is used for these cases. The quadratic formula yields all the answers, including both real and imaginary numbers.

When using the quadratic equation, first make sure that the equation is set to be equal to zero before computing. Otherwise, the formula will not work. Because of the +- sign between the two terms in the numerator, expect to have two different real or imaginary numbers as answers. An exception to this is when the value of the second term is zero, which in such case, the formula yields a one repeated root only.

Aside from the quadratic formula, some other algebra laws and shortcuts used by mathematicians are the laws of exponents and special factoring rules. The laws of exponents come in handy when manipulating exponents in an equation, while special factoring rules, such as the perfect square trinomial, difference of two squares and sum and difference of two cubes, help in simplifying and factoring polynomials without having to divide using the long method all the time.

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