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Adding, Subtracting, and Multiplying Radical Expressions. Section 8.4 MATH 171-460 Mr. Keltner. Adding & Subtracting Like Radicals. Recall that terms such as 8 x 2 and -5 x 2 are considered like terms because they have identical variable parts.

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## Adding, Subtracting, and Multiplying Radical Expressions

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**Adding, Subtracting, and Multiplying Radical Expressions**Section 8.4 MATH 171-460 Mr. Keltner**Adding & Subtracting Like Radicals**• Recall that terms such as 8x2 and -5x2 are considered like terms because they have identical variable parts. • When we combine like terms, we simply combine their coefficients, such as 8x2 + (-5x2) = 3x2. • Like radicals are ones that have the same index and radicand. • Example: and are like radicals.**Example 1:Simplifying Like Radicals**• Simplify.**Un-Like Radicals: What to do?**• If radicals do not happen to be like radicals, try simplifying each radical term first. • It may just work out that the radicals had more in common than it first appeared.**Example 2: Simplifying Un-Like Radicals**• Simplify, assuming all variables represent nonnegative values.**Simplifying using other strategies**• We can also simplify radical expressions by: • Using the Distributive Property • Multiplying a conjugate pair (quantities that are the same except for the sign between terms, such as (8-√3) and (8+√3). • Squaring a binomial in the form (a + b)2 • FOIL-ing a pair of binomials**Example 3:Multiplying Expressions**• Multiply each expression and simplify.**Expressions with Mixed Operations**• In some instances, it may be necessary to simplify an expression with any combination of addition, subtraction, multiplication, and division. • It is best to simplify using the Product and Quotient properties first. • Example 4: Simplify the expression:**Assessment**Pgs. 572 - 575: #’s 7 - 98, multiples of 7

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