Chapter 9 Radical Functions
Chapter 9 Radical Functions
Chapter 9 Radical Functions
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Homework 9.2<br />
SSM: Intermediate Algebra<br />
3 3<br />
19. 7( x + 1) − 7( x −1)<br />
3 3<br />
3 3<br />
3 3<br />
( )<br />
= 7 ⋅ x + 7 ⋅1− 7 ⋅ x − 7 −1<br />
= 7 x + 7 − 7 x + 7<br />
= 7 x − 7 x + 7 + 7<br />
= 14<br />
21. 25x + 4x = 25 x + 4 x<br />
= 5 x + 2 x<br />
= 7 x<br />
23. 3 20x + 2 45x = 3 4⋅ 5x + 2 9⋅5x<br />
= 3 4 5x<br />
+ 2 9 5x<br />
= 3⋅ 2 5x<br />
+ 2⋅3 5x<br />
= 6 5x<br />
+ 6 5x<br />
= 12 5x<br />
25.<br />
27.<br />
3 2<br />
5 x − x 49x = 5 x ⋅ x − x 49 ⋅ x<br />
2<br />
= 5 x x − x 49 x<br />
= 5x x − 7x x<br />
( 5 7)<br />
= −<br />
2 2<br />
= −2x<br />
x<br />
3 81x − 2 100x = 3⋅9x − 2⋅10x<br />
x<br />
x<br />
= 27x<br />
− 20x<br />
= 7x<br />
33.<br />
35.<br />
37.<br />
4 11 4 7 4 8 3 4 4 3<br />
16x − 3x x = 16x ⋅ x − 3x x ⋅ x<br />
4 8 4 3 4 4 4 3<br />
= 16x x − 3x x x<br />
2 4 3 2 4 3<br />
= 2x x − 3x x<br />
( 2 3)<br />
= −<br />
= −x<br />
2<br />
x<br />
2 4 3<br />
3 x ⋅ 2 x = 3⋅ 2⋅ x ⋅ x<br />
= 6 x ⋅ x<br />
= 6<br />
x<br />
x<br />
2<br />
2 4 3<br />
= 6x<br />
−2 5x ⋅ 4 3x = −2⋅ 4⋅ 5x ⋅ 3x<br />
= −8 5x<br />
⋅3x<br />
39. ( )<br />
= −8 15x<br />
= −8 15 x<br />
= −8x<br />
15<br />
2 7x 7x + 2x = 2 7x ⋅ 7x + 2 7x ⋅ 2x<br />
2<br />
x<br />
= 2 7x ⋅ 7x + 2 7x ⋅ 2x<br />
2 2<br />
= 2 49x<br />
+ 2 14x<br />
2 2<br />
= 2 49 x + 2 14<br />
= 2⋅ 7x<br />
+ 2x<br />
14<br />
= 14x<br />
+ 2x<br />
14<br />
x<br />
29.<br />
31.<br />
3 2<br />
12x + x 75x = 4x ⋅ 3x + x 25⋅3x<br />
2<br />
= 4x 3x + x 25 3x<br />
= 2x 3x + 5x 3x<br />
( )<br />
= 2 + 5 x 3x<br />
= 7x<br />
3x<br />
3 5 3 2 3 3 2 3 2<br />
27x − x 8x = 27x ⋅ x − x 8⋅<br />
x<br />
3 3 3 2 3 3 2<br />
= 27x x − x 8 x<br />
3 2 3 2<br />
= 3x x − 2x x<br />
( 3 2)<br />
= −<br />
= x<br />
3 2<br />
x<br />
x<br />
3 2<br />
x<br />
41. ( 6 − 2 x )( 5 x − 4)<br />
2<br />
( )<br />
= 6⋅5 x − 2 x ⋅5 x − 6⋅ 4 − 2 x −4<br />
= 30 x −10 x − 24 + 8 x<br />
= − 10x + 30 x + 8 x − 24<br />
= − 10x<br />
+ 38 x − 24<br />
43. ( 2 x + 1)( x − 4)<br />
= 2 x ⋅ x + 1⋅ x − 2 x ⋅ 4 −1⋅<br />
4<br />
2<br />
= 2 x + x − 8 x − 4<br />
( )<br />
= 2x<br />
+ 1− 8 x − 4<br />
= 2x<br />
− 7 x − 4<br />
278