1001 Algebra Problems.PDF

111. a.The expression described by the phrase “3x^2
     is multiplied by the quantity 2x^3 yraised to the
     fourth power” can be expressed symbolically
     as (3x^2 )(2x^3 y)^4 , which is simplified as follows:
     (3x^2 )(2x^3 y)^4 =(3x^2 )(2^4 x^12 y^4 ) =48x^14 y^4


112. b.“The product of –9p^3 rand the quantity
     5 p– 6r” can be expressed symbolically as
     (–9p^3 r)(5p– 6r), which is simplified using
     the distributive property as follows:
     (–9p^3 r)(5p– 6r) = –45p^4 r+ 54p^3 r^2.

Set 8 (Page 13)

113. c. 5 ab^4 – ab^4 = 4ab^4

114. a. 5 c^2 +3c– 2 c^2 +4 – 7 c= (5c^2 – 2c^2 ) +
     (3c– 7c) + 4 = 3c^2 – 4c+ 4


115. c. – 5(x– ( – 3y)) + 4(2y+x) = – 5(x+ 3y) +
     4(2y+x) = – 5x– 15y+ 8y+ 4x= – x– 7y


116. b.Gather like terms, as follows: 3x^2 + 4ax– 8a^2

+ 7x^2 – 2ax+ 7a^2 = (3x^2 + 7x^2 ) + 4ax– 2ax) +

(–8a^2 + 7a^2 ) = 10x^2 + 2ax– a^2

117. d.The base expressions of the three terms used
     to form the sum 9m^3 n+ 8mn^3 + 2m^3 n^3 are dif-
     ferent. So, they cannot be combined.


118. d. – 7 g^6 + 9h+ 2h– 8g^6 =(–7g^6 – 8g^6 ) +
     (9h+ 2h) = –15g^6 + 11h


119. b.(2x^2 )(4y^2 ) + 6x^2 y^2 = 8x^2 y^2 + 6x^2 y^2 = 14x^2 y^2


120. c.(5a^2  3 ab) + 2a^3 b= 15a^3 b+2a^3 b= 17a^3 b


121. b. 2 x– 3–– (x^3 )–1= – – =

- = x–3–3x–5

122. a.(ab^2 )^3 + 2b^2 – (4a)^3 b^6 = a^3 b^6 + 2b^2 – 4^3 a^3 b^6
     = 2b^2 – 63a^3 b^6


123. b. + ^89 (x^2 )^2 = + =

+ = + = x^4

124. b.–(–a–2bc–3)–2+ 5–2= –(a^4 b–2c^6 ) +

(^5) = – + =

125. c.3(z+ 1)^2 w^3 –

= 3(z+ 1)^2 w^3 – 2w(z+ 1)((z+ 1)w^2 )

= 3(z+ 1)^2 w^3 – 2(z+ 1)^2 w^3

= (z+ 1)^2 w^3

126. a.
     –2(4x+1)

(^5) y–5–

–2
= –– 
–2

= (– – )– 2

= – 

–2

= – 

2

=

=

127. b.
     4 z((xy–2)–3+ (x–3y^6 ))–1– ^1 z^2 xy 3
     ^6
     

–1

= 4z((x–^3 y^6 ) + (x– 3y^6 ))–1– ^2 zxy 3

^6



–1

= 4z(2(x–^3 y^6 ))–1– ^2 zxy 3

^6



–1

= 4z( 2 –1x^3 y– 6))–1–

= –

=

128. a.
     (0.2x–2)–1 + ^25 x^2 –

=  120 x–2

–1

+ ^25 x^2 – ^54 xx

4

 2

= 5x^2 + ^25 x^2 – ^54 x^2

= (^1200 ^0 +  280 – ^2250 )x^2

= ^8230 x^2

^5 x^4

(2x)^2

^3 zx^3

2 y^6

zx^3

2 y^6

^4 zx^3

2 y^6

zx^3

2 y^6

y^10

16(4x+ 1)^10

(–1)^2 y^10

42 (4x+ 1)^10

y^5

4(4x+ 1)^5

4(4x+1)^5

y^5

2(4x+ 1)^5

y^5

2(4x+1)^5

y^5

^2 y(4x+ 1)^2

((4x+ 1)–3y^6

2(4x+1)^5

y^5

^2 y(4x+ 1)^2

((4x+ 1)y–2)–3

^2 w(z+ 1)

((z+ 1)w^2 )–1

^4 a^4 c^6

b^2

^5 a^4 c^6

b^2

a^4 c^6

b^2

b–2

a–4c–6

b

a^2 c^3

^8 x^4

9

x^4

9

^8 x^4

9

x^2

(–3)^2 x–2

^8 x^4

9

x^2

(–3x–1)^2

(–3x–1)–2

x–2

^3

x^5

^1

x^3

^1

x^3

^3

x^5

^2

x^3

^3 x–1

x^4

ANSWERS & EXPLANATIONS–