Rather than computing each exponential term and multiplying or dividing manually, simply add exponents when multiplying and subtract when dividing to save time. Some algebraic expressions require multiplying or dividing exponential terms. Since any fraction with "1" in the denominator is equal to the terms in the numerator, we can say that our original fraction can be simplified to 3x 2 + 9x - 1.Īdd exponents when multiplying two exponential terms subtract when dividing.Dividing the numerator and denominator by 3, we get: (3x 2 + 9x - 1)/1. Notice that now, both the numerator and the denominator share the coefficient 3.Let's substitute the factored form of our original expression for the expression in the numerator: (3(3x 2 + 9x - 1))/3.We can use factoring to simplify this fraction. This fraction would look like this: (9x 2 + 27x - 3)/3. Let's say our original example expression, 9x 2 + 27x - 3, is the numerator of a larger fraction with 3 in the denominator.One of the easiest of these involves taking advantage of the fact that multiplying a fraction's numerator and denominator by the same number gives an equivalent fraction. In fact, factoring allows a mathematician to perform a variety of tricks to simplify an expression. You may now be wondering why factoring is useful if, after removing the greatest common factor, the new expression must be multiplied by it again. Now, since the only operations left are addition and subtraction, we can combine like terms. First, let's perform the arithmetic operations in the expression in accordance with the order of operations to obtain terms we can use. It would be incorrect to immediately identify 3x and 2x as like terms and combine them because the parentheses in the expression dictate that we're supposed to do other operations first. In these cases, follow the order of operations, performing operations on the terms in your expression as necessary until only addition and subtraction operations remain. However, in more complex expressions, like ones that involve terms in parentheses, fractions, and radicals, like terms which can be combined may not be immediately apparent. In extremely simple expressions like the one dealt with in the example problems above, identifying like terms is simple. Obey the order of operation when combining like terms.
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