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.

52 + 32 = (5 + 3)2 = 82

-72x + 32x = (-7 + 3)2x = -42x

82 + 73 cannot be simplified because the radicals do not have like radicands

Simplify the following:

48 – 102

= =82 – 102 -22

818x – 232x

= =242x – 82x 162x

Simplify each of the following expressions:

= 44 2 – 102

= 89 2x – 216 2x

312x3 – 2x3x

= =6x3x – 2x3x 4x3x

Simplify each of the following expressions:

= 34x23x – 2x3x

2a8ab2 – 2b2a3

=

=

4ab2a – 2ab2a

2ab2a

= 2a4b22a – 2ba22a

Simplify each of the following:

2x8y – 32x2y + 232x2y

= 4x2y – 3x2y + 8x2y

= 9x2y

= 2x42y – 3x22y + 216x22y

Simplify each of the following:

227a5 – 4a12a3 + a275a

= 6a23a – 8a23a + 5a23a

= 3a23a

= 29a43a – 4a4a23a + a2253a