1001 Algebra Problems.PDF

506. b.

 = 

=  =

507. b.

 = 

 = 

=

508. c.

(4x^2 – 8x– 5)  =

(2x+ 1)(2x– 5)  =

(2x+ 1)(2x– 5)[–(2x– 5)] = (2x+ 1)

(2x+ 5) = –(2x+ 1)

509. a.
       =

  =

=

= 

=

510. a.(x– 3) = (x– 3) =

(x– 3) =

511. b.

   = 

= =

=

512. d.
     =



=

Set 33 (Page 82)

513. b.

1 – ^14 +  – 

2

= 1 – (^34  )

^14 +

2

= 1 – (^34  196 )^14 + ^8116 =

1 – ^34 ^196 ^14 + ^8116 = 1 –  1 ^43 ^14 + ^8116 =

1 – ^13 + ^8116 = =

514. b. = = 4 = ^137 


515. b.

 +  =

 –  =

 =



= –(x+ 2)(x+ 5)

–(5 – x)(5 + x)

3 x– 1

(3x– 1)(x+ 2)

x– 5

–(5 – x)(5 + x)

3 x– 1

^3 x(x+ 2) – (x+ 2)

x– 5

(5 – x)(5 + x)

3 x– 1

x+ 2

x– 5

^3 x(x+ 2)

x– 5

^3 x– 1

25 – x^2

2 + x

5 – x

^3 x^2 + 6x

x– 5

^1172 

 1

4 

 182 +  192 

 3

4 – ^24 

^23 + ^34 

 3

4 – ^12 

^275

48

48 – 16 + 243

48

10 – 1

4

^9

16

^1

4

^5

2

^34 



196 

x– 2

x^2

(x– 2)(x+ 2)

x(x+ 2)

(3x+ 1)(2x+ 1)

x(3x+ 1)

(2x+ 1)(x+ 3)

(2x+ 1)(2x+ 1)

x+ 2

(x+ 2)(x+ 3)

x^2 – 4

x^2 + 2x

^6 x^2 + 5x+ 1

3 x^2 + x

^2 x^2 + 7x+ 3

4 x^2 + 4x+ 1

x+ 2

x^2 + 5x+ 6

^25 x^3 y^3

4(x+ 1)

^25 x^4 y^4

4 xy(x+1)

^15 x^2 y^2

3 x(x+ 1)

^10 xy^2

2(x– 1)

x(x– 1)

4 y

^15 x^2 y^2

3 x^2 + 3x

^10 xy^2

2 x– 2

x^2 – x

4 y

^3 x^2 + 3x

15 x^2 y^2

^10 xy^2

2 x– 2

x^2 – x

4 y

x

x+ 6

x

(x– 3)(x+ 6)

x

x^2 + 3x–18

x^2 + 3x– 18

x

(a+ b)^2

ab

(a+ b)(a+ b)

b(a– 3b)

(a– 3b)

a

(a+ b)(a+ b)

b(a– 3b)

(2a– b)(a– 3b)

a(a+ b)

(a+ b)

(2a– b)

(a+ b)(a+ b)

b(a– 3b)

(2a– b)(a– 3b)

a(a+ b)

(a– b)(a+ b)

(2a– b)(a– b)

a^2 + 2ab^2 + b^2

ab– 3b^2

^2 a^2 – 7ab+ 3b^2

a^2 +ab

a^2 – b^2

2 a^2 – 3ab+ b^2

ab– 3b^2

a^2 + 2ab+ b^2

^2 a^2 – 7ab+ 3b^2

a^2 +ab

a^2 – b^2

2 a^2 – 3ab+ b^2

^1

–(2x– 5)

(2x– 5)(x+ 1)

x– 3

–(x–3)

x+ 1

^2 x^2 – 3x– 5

x– 3

–(x– 3)

x+ 1

–2(x+ 2)

x^2

(x+ 2)

x

^2

–(x– 1)

(x– 1)

x

(x+2)(x– 1)

x(x–1)

2(x+ 1)

(1 –x)(1 + x)

(x– 1)(x+ 1)

x(x+ 1)

x^2 + x– 2

x^2 – x

^2 x+

1 – x^2

x^2 – 1

x^2 + x

(2x+ 1)(x– 2)

2(x– 1)(x+ 1)

^2 x(2x– 2)

(2x+ 1)(x+ 1)

(2x+ 1)^2

4 x(x– 1)

^2 x^2 – 2x

2 x^2 + 3x+ 1

(^4) x^2 + 4x+ 1
4 x^2 – 4x
^2 x^2 + 3x+ 1
2 x^2 – 2x
^4 x^2 + 4x+ 1
4 x^2 – 4x
ANSWERS & EXPLANATIONS–