1001 Algebra Problems.PDF

516. d.

 – h=

 – –  h=

h= h=

h^1 =

517. d. = = abb+1baa+ 1 = ab


518. a.

= =

= = 2(6 3 – x)

519. c.

 =

=

= =

= = =

• (x– 1)

520. a.

1 – = 1 – = 1 – ( 5 xx+^5  5 ) =

1 – x+x 5 = xx++ 55 – x+x 5 = x+^5  5

521. d.

= = = = = 

=– 2 a^82 a+8= a (^24) +a 4

522. a.

=

=

=

=  =  =

 =  = –  2 x

523. a.(a–1+ b–1)–1=^1 a+ ^1 b

–1

= ba+ba

–1

= ba+ba

524. b. = = = yx–yxyx+yx= yy+–xx

yx–yx

y

x+yx

^1 x– ^1 y

 1

x+ ^1 y

x–1–y–1

x–1+ y–1

x^2 – 4

2

x

–(x^2 – 4)

x^2 – 4

2 x

x^2

4 – x^2

(x+ 2)(x– 2)

2 x

x^2

4 – x^2

(x+ 2)(x– 2)

2 x

x^2

4–x^2

4–^44 – +x^2 x^2

(xx–+^2 2)+(xx–+ 22 )

-^4 x^2 – ^44 – –xx
^22

(x+x2)–(^2 x–2)+ (x+x 2 +)(^2 x–2)

4–^4 x 2 – 1



x+^1  2 + x–^1  2

(a+ 2)(a– 2)

a^2 – 4a+ 4 + (a^2 + 4a+ 4)

a^2 – 4a+ 4 – (a^2 + 4a+ 4)

(a+ 2)(a– 2)

a^2 – 4a+ 4 + (a^2 + 4a+ 4)

(a+ 2)(a– 2)

a^2 – 4a+ 4 – (a^2 + 4a+ 4)

(a+ 2)(a– 2)

(a– 2)(a– 2) + (a+ 2)(a+ 2)

(a+ 2)(a– 2)

(a– 2)(a– 2) – (a+ 2)(a– 2)

(a+ 2)(a– 2)

• ((aa++ 22 ))((aa–+2 2 ))
  + (
  (aa++^22 ))((aa+–2^2 ))

((aa–2+ 2 ))((aa––^22 ))

((aa+–2 2 ))((aa––^22 ))

aa+–2 2 – aa+–2^2



aa+–2 2 + aa+–2^2

^5 x

5+ 5 x

 5 x

1 + 

5 x

–(2x– 7)(x– 1)

2 x– 7

–(2x^2 –9x+ 7)

x– 7

–2x^2 + 9x– 7

2 x– 7

^5 x– 5 – 2x^2 + 4x– 2

2 x– 7

5(x– 1) – 2(x– 1)^2

2(x– 1) –5

(x–^5  1) 3  (x– 1)^4 – (x–^2  1) 3 (x– 1)^4

– 

(x–^5 1)^4 (x– 1)^4

(x– 1)^4

(x– 1)^4

(x–^5 1) 3 – (x–^2 1) 2



(x–^2 1)^3 – (x–^5 1)^4

12 – 2x

5 – 2

4 x^3 x– 4x^12 



4 x 45 x– 4x 21 x

4 x^3 x– ^12 



4 x 45 x–  21 x

^3 x– ^12 

 5

4 x–  21 x

abb+ ^1 b

b

aa+ ^1 a

a+ ^1 b

b+  1

a

–(2x+ h)

x^2 (x+ h)^2

–h(2x+ h)

x^2 (x+ h)^2

x^2 – x^2 – 2hx– h^2

x^2 (x+h)^2

x^2 – (x+ h)^2

x^2 (x+ h)^2

(x+ h)^2

(x+ h)^2

^1

x^2

x^2

x^2

^1

(x+ h)^2

^1

x^2

^1

(x+ h)^2

ANSWERS & EXPLANATIONS–