 # Math 010 Unit 6 Lesson 7. Radical expressions can only be combined by addition or subtraction if they have like radicands. The Distributive Property can.

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Math 010 Unit 6 Lesson 7

Radical expressions can only be combined by addition or subtraction if they have like radicands. The Distributive Property can be used to simplify such expressions. 5  2 + 3  2 = (5 + 3)  2 = 8282 -7  2x + 3  2x = (-7 + 3)  2x = -4  2x 8  2 + 7  3 cannot be simplified because the radicals do not have like radicands Simplify the following:

4  8 – 10  2 = = 8  2 – 10  2-2  2 8  18x – 2  32x = = 24  2x – 8  2x16  2x Simplify each of the following expressions: = 4  4  2 – 10  2 = 8  9  2x – 2  16  2x

3  12x 3 – 2x  3x = = 6x  3x – 2x  3x4x  3x Simplify each of the following expressions: = 3  4x 2  3x– 2x  3x 2a  8ab 2 – 2b  2a 3 = = 4ab  2a – 2ab  2a 2ab  2a = 2a  4b 2  2a– 2b  a 2  2a

Simplify each of the following: 2x  8y – 3  2x 2 y + 2  32x 2 y = 4x  2y – 3x  2y + 8x  2y = 9x  2y = 2x  4  2y – 3  x 2  2y + 2  16x 2  2y

Simplify each of the following: 2  27a 5 – 4a  12a 3 + a 2  75a = 6a 2  3a – 8a 2  3a + 5a 2  3a = 3a 2  3a = 2  9a 4  3a– 4a  4a 2  3a+ a 2  25  3a