Algebra 1 Common Core Student Edition, Grade 8-9

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Simplify each product using the FOIL method.

20. (a + 8)(a - 2) 21. (x + 4)(4x - 5)


21. (b - 3)(fc - 9) 24. (5m - 2)(m + 3)


22. (3h + 2)(6h - 5) 27. (4w + 13)(m + 2)


23. Geometry W hat is th e total surface area of th e cylinder?
    W rite your answ er as a polynom ial in stan d ard form.


24. Design Ih e radius of a cylindrical gift box is (2x + 3) in.
    The height of the gift box is twice th e radius. W hat is
    th e surface area of th e cylinder? W rite your answ er as a
    polynom ial in stan d ard form.

^ See Problem 3.

22. 0 - 6 ) ( f c + 8 )


23. (9z + 4)(5z - 3)


24. (8c - l)(6 c - 7)

x 1 2 ^ See Problem 4.

x+ 5

1

Simplify each product.

31. (x + 5)(x2 - 3 x + 1)


32. (2a2 + 4a + 5)(5a - 4)

See Problem 5.

32. O 2 — 4fc + 3 ) 0 — 2)


33. (2g+7)(3g2 ~ 5 g + 2 )


34. Sports A school’s rectangular athletic fields currently have a length of 125 yd an d
    a w idth of 75 yd. The school plans to expand b o th th e length an d th e w idth of the
    fields by x yards. W hat polynom ial in stan d ard form rep resen ts th e area of th e
    expanded athletic field?

Simplify each product. Write in standard form.

36. (x2 + l)(x - 3) 37. {-n2 — 1)(« + 3)
    39. (2m2 + l)(m + 5) 40. (c2 - 4)(2c + 3)


37. Error Analysis D escribe an d correct th e error m ad e in
    finding th e product.


38. Reasoning Is th e p ro d u ct of two polynom ials always a
    polynomial? Explain.

(X -

38. {b2 - 1 \b 2 + 3)


39. (4z2 + l)(z + 3z2)

-= i(3 x U -

44. Think About a Plan You are p lan n in g a rectangular dining pavilion. Its length
    is three tim es its w idth x. You w an t a stone walkway th a t is 3 ft wide a ro u n d th e
    pavilion. You have enough stones to cover 396 ft2 an d w an t to use th em all in the
    walkway. W hat should th e dim ensions of th e pavilion be?
    
    
    • Can you draw a diagram th a t represents this situation?
    
    
    • How can you write a variable expression for th e area of th e walkway?
    
    
    
    


45. a. Simplify each p air of products.
    i. (x + l)(x + 1) ii. (x + l)(x + 2) iii. (x + l)(x + 3)
    11 - 1 1 11 • 12 11 • 13
    b. Reasoning W hat are th e sim ilarities betw een your two answ ers in each pair
    of products?


46. Geometry The dim ensions of a rectangular prism are n, n + 7, an d n + 8. Use the
    formula V = (w h to write a polynom ial in standard form for th e volum e of the prism.

502 Chapter 8 Po l y n o m i al s an d Fact o r i n g