Algebra 1 Common Core Student Edition, Grade 8-9

Simplify. Write each answer in standard form.

44. (5 x 2 - 3x + 7x) + (9 x 2 + 2x2 + 7 x) 45. (y3 - Ay2 - 2 ) - ( 6 y 3 + 4 - 6 y 2 )


45. ( —9 r 3 + 2r — l ) - ( - 5 r 2 + r + 8) 47. (3z3 ~ 4 z + 7z2) + (8z2 - 6 z ~ 5 )


46. a. Is th e sum of two polynom ials always a polynom ial? Explain.
    b. Is the difference of two polynom ials always a polynom ial? Explain.

Challenge 49. a. Write th e equations for line p an d line q. Use slope-intercept form.
b. Use your eq u atio n s from p a rt (a) to w rite a function for the
vertical distance D(x) betw een points on lines p an d q w i t h
the same x-value.
c. For what value of x does D(x) equal zero?
d. Reasoning How does th e x-value in p a rt (c) relate to the graph?

Simplify each expression.

50. [ab2 + ba3) + ( 4 a3b - ab2 - 5ab)


51. (9pqe - l l p Aq) - (~ 5pq6 + p 4q 4)

Apply What You've Learned

Look back at Kelly’s an d R oberto’s original plots o n page 485. C hoose from the

following words, num bers, an d expressions to com plete th e sentences below.

MATHEMATICAL

PRACTICES

MP 6

monomial binomial trinomial

x+2 x2 + 2 x + 6 2x + 6

Two polynom ials th a t rep resen t th e length a n d w idth of Kelly’s plot are

a.? a n d b.?. Each of th ese polynom ials is an exam ple of a c.?. The

polynom ial th at rep resen ts th e area of R oberto’s flower b e d is d. _?_. T his

polynom ial is an exam ple of a e. _?_. The degree of this polynom ial is f. J_

PowerAlgebra.com Lesso n 8-1 Adding and Subtracting Polynomials^491