Algebra 1 Common Core Student Edition, Grade 8-9

J Lesso n Ch eck^

Do y o u k n o w H OW?

Simplify each expression. State any excluded values.

1 .3x + 9 x + 3 2.

x2 - 2x 15

3. The two rectangles below have th e sam e area. W hat
   is a sim plified expression for th e length ( of the
   rectangle on the right?

2x + 4

2 x

Do y o u UN DERSTAN D?

MAIHEMAIICAL

— ------------------------------- PRACTICES

4. Vocabulary Is each expression a rational expression?
   Explain your reasoning.
   Vx + 2 y
   x 2 + 4 b.y- i


5. Writing W hen simplifying a rational expression, why
   may it be necessary to exclude values? Explain.


6. R e a s o n i n g Suppose n e ith e r th e n u m era to r n o r
   th e d en o m in ato r of a rational expression can be
   factored. Is th e expression necessarily in simplified
   form? Explain.


7. Are th e given factors opposites? Explain.
   a. 3 — x; x — 3 b. 2 — y; — y + 2

Practice

sj g P Pract ice an d Pro b lem - So lvin g Ex er ci ses

Simplify each expression. State any excluded values

8.

11.

14.

17.

20.

23.

26.

MAIHEMATICAL

PRA CTICES

^ See Problems 1,2, and 3.

6a + 9

12 9.

4X3

28x4

10 .6m 2m —— 15 5

2p — 24

Ap- 48 12.

3x2 — 9x

x — 3 13.

3x+ 6

3x2

2x2 + 2x 15. 2b-8 16. m^ + 6

3x2 + 3x b^2 - 16 m2 — m — A2

w2 + Iw

w2 - 49

18.a^2 + 5a2a + 5 +^1 19.m2m2^ + + 7m 6m+ + 8^12

c2 — 6c + 8 21 .b2 + 8b+^1522. m +^4

c2 + c — 6 b +^5 m2 + 2m —^8

5 — 4« 24. 12 - At 25.Am -^8

4n - 5 t2 - 2 t - 3 4 — 2m

m — (^2) 27. v — (^5) 28.^4 — w
4-2 m 25 - v 2 w2 - 8w + 16

29. Geometry The length of a rectangular prism is 5 m ore th a n twice th e w idth w.
    The volume of the prism is 2w 3 + 7 w 2 + 5 w. W hat is a sim plified expression
    for th e h eight of th e prism?


30. Geometry Rectangle A h as length 2x + 6 and w idth 3x. Rectangle B has length
    x + 2 an d an area 12 square u n its greater th a n Rectangle A's area. W hat is a
    sim plified expression for th e w idth of Rectangle B?

4^ See Problem 4.

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