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Algebraic Expression Questions and Answers

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  • Last Update June 19, 2021

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Algebraic expressions

  1. Simplify (3mks)
  1. Five year ago, a mother’s age was four times that of her daughter. In four years to come,

she will be 2 ½ times the age of her daughter. Calculate the sum of their present ages




 

  1. Mutua bought 160 trays of 8 eggs each at shs.150 per tray. On transportation 12 eggs

broke. He later discovered that 20 eggs were rotten. If he sold the rest at shs.180 per

tray, how much profit did he  make?

  1. Simplify;

(a) 6a – 2b + 7a – 4b + 2

(b) 2x – 2             3x + 2




2x                    4x

 

  1. Simplify  6x2y2 + 13xy-5

3x2y2 – 13xy + 4

 

  1. Given that x + y = 8 and x2 + y2 = 24

Find;

(a) the value of x2 + 2xy + y2

(b) Find the value of ; 2xy

(c) x2 – 2xy + y2

(d) x – y

(e) Value of x and y




  1. Simplify the expression.

6x2  + 35x – 6

            2x2 – 72

 

  1. Simplify the expression

2/3 (3x -2) – ¾ (2x -2)

 

  1. Simplify by factorizing completely:

   4y2 – x2




2x2 – yx -6y2

  1. Simplify as far as possible.

3             –    1

              x – y            x + y

 

  1. By calculation, find the coordinates of the intersection of the graphs y = x2 + 2x -5

and y = 3x +1

 

  1. Simplify:

(a)          y2 + 2y       = ¼

y3 – y2 – 6y

(b) hence solve:- y2 + 2y = ¼




                                    y3 – y2 – 6y

 

  1. A rectangular field measures 63.9m by 104.6metres find the minimum number of poles to be

erected for fencing if they are to be at most 2.4meters apart.

 

  1. Factorize completely the expression

75x2 – 27y2

 

  1. Every time an insect jumps forward the distance covered is half of the previous jump.

If the insect initially jumped 8.4cm, calculate

(i) To the nearest two decimal places distance of the sixth jump

(ii) The total distance covered after the sixth jump




  1. Simplify  P3 –Pq2 + P2q – q3

P2 + 2pq + q2

 

  1. Simplify the expression:- 9x2 – 4y2

12x2 + yx – 6y2

  1. Given that (x-3) (Ax²+bx+c) = x³-7x-6, find the value of A, B and C

 

  1. a) solve for y in 8x(2²)ʸ=6×2ʸ-1
  2. b) Simplify completely  2x²-98       ÷     x+7

3x²-16x-35         3x+5




  1. Simplify the expression.:

 

4x2 – y2

2x2 – 7xy + 3y2

 

  1. Simplify P2 -2Pq + q2

P3 –Pq2+ P2q – q3

 

  1. The sum of two numbers is 15. The difference between five times the first number and

three times  the second number is 19. Find the two numbers

 

  1. Simplify the following expressions by reducing it to a single fraction

2x – 5 –  1 – xx – 4

4          3          2




  1. Simplify the expression:- 3a2 + 4ab + b2           

4a2 + 3ab – b2

 

ANSWERS for Algebraic Expression

  1. Algebraic expressions

 Let the daughter’s age 5yrs ago be x 

Mother 4x

 come;

Daughter = x + 9

Mother  = 4x+ 9

4x + 9 = 5/2 (x +9)

4x + 9 = 2.5x + 22.5

1.5x = 13.5

                      x = 9

Mother = 41yrs

14 + 41 =55

 

  1.  B.P = 160 x 50 = 24000

S.P = ((160 x 8) – (20 + 12)) x 180

                                     8

                           = 28080

Profit = 28080 – 24000      = Shs.4080

 

 

  1. a) 6a + 7a – 2b – 4b + 2

                   = 13a – 6b + 2

 

  1. b) 2x – 23x + 2 = 2(2x – 2) – (3x + 2)

                   2x            4x                   4x

                       = 4x – 3x – 4 – 2

                                   4x

                        = x – 6

                             4x

 

  1. 6u2y2 + 13uy – 5 = (2uy + 5) (3xy – 1)

3u2y2 – 13uy + X  = (uy – 4)  (3xy – 1)

   (2xy +5)     (3xy – 1)

  (uy – 4)        (3xy -1)

 

                              = 2xy + 5

                                  Uy – 4

 

  1. a) From x + y and x2 = y2 = 34

                             X = 8 – y

                        Substituting for x in x2 – y2 = 34

                         (8 – y) (8 – y) + y2 = 34

                        64 – 8y – 8y + y2 + y2 = 34

64 – 16y + 2y2 = 34

 

2y2 – 16y + 64 – 34 = 0

2y2 – 16y + 30 = 0

y2 = 8y + 15 = 0

y (y – 3) – 5 (y-3) = 0   (y-5) (y – 3)

                                        y is either 5 or 3

but x – y = 8

                         x is either 5 0r 3

\ x2 + 2xy + y2 = 32 + 2 x 3 x 5 + 25

                                                  = 9 + 30 + 25 = 64

 

  1. b) 2xy = 2 x 3 x 5 = 30
  2. c) x2 – 2xy + y2 = 9 – 2 x 3 x 5 + 25 = 4

 




  1. d) x = y = 8 and x2 + y2 = 34

                         x = 8 – y

                        (8 – y)2 + y2 = 34

y2 – 8y + 15 = 0

y2 – 3y – 5y + 15 = 0

y(y -3) – 5(y – 3)

  (y-3) = o  y = 3

             (y-5) = 0  y = 5

 

x + 3 = 8, x = 5 or x + 5 = 8

                               x = 3

\ x is either 3 or 5

             y is either 3 0r 5

 

  1. 6x2 + 35x – 6

                2x2 – 72

  = 6x(x -+ 6) -1(x + 6)

                         2(x2 – 36)

             = (6x – 1) (x + 6)

               2(x – 6) (x + 6)

            = 6x – 1

              2(x – 6)

  1. 8. 2/5 (3x -2) – ¾ (2x -2)

= 8(3x-2) -9(2x-2)


= 24 x -16 – 18x + 18
                         12

= 6x + 2

               12

= 2(3x +1)

                       12

= 3x + 1

               6

 

  1. Numerator:

4y2 – x2 = (2y +x) (2y – x)

Denominator :

2x2 + 4yx + 3yx – 6y2

= (2x2 – 4yx) + (3yx – 6y2)

=   2x(x-2y) + 3y(x-2y)

= (2xx+3y) (x-2y)

Combining : (2y + x) (2y-x)

                                    (2x+3y) (x-2y)

2x + 3y or -2x -3y

             2y + x        2y + x

 




  1. 3(x + y) – (x –y)

                 X 2  – y2

            = 3x + 3y – x + y

                        x2  –  y2

             = 2(x +2y)

                  x2 -y2

 

  1. x2 + 2x – 5 = 3x +1

x2 – x – 6 – 6 =0

(x+2) (x-3) = 0

x =-2 or x = 3

When x =-2,   y = 3x – 2 + 1 = -5  Point (-2, -5)

When x = 3,   y = 3x x 3 +1 = 10   Point (3, 10)

 

  1. (a)  y(y + 2)

                        y(y2 – y -60

             y(y+2)            =    y + 2

             y(y2 – y-6)        (y+2) (y-3)

 

(b) y + 2     = ¼

    (y + 2) (y-3)

4y + 8 = y2 – y – 6

y2 – 5y – 14 = 0

(y-7)(y+2)= 0

y=7

y=-2

 

  1. 104.6 = 44 x 2

            2.4

63.9 = 26 x 2

            2.4

= 88 + 54= 142

  1. 3 ( 25 x2 – 9y2)

3 (5x + 3y) (5x – 3y)

 

 

  1. i) d = 8.4                            r = ½

            6th jump = 8( ½ )6-1

              8.4/32

 

              = 0.2625 = 0.26cm

 

  1. ii) 56 = 4 (1 – ( ½ ) 6

                                     1 – ½

               = 8.4 x 63 x 2

                          64

             = 16.54 cm

 

  1. Factorizing the numerator

= p(p2 – q2) + q(p2-q)

= (p+q) (p2-q2)

= (p+q) (p+q) n(p-q)

Factorising the denominator

(p+q) (p+q)

Numerator    = p – q

Denominator

 

  1. ( 3x  + 2y )   ( 3x  – 2y ) 

            ( 3x  + 2y )   ( 3x  – 2y ) 

              3x + 2y

             4x + 3y

 

  1. (x – 3) (AX2 +BX + C) = x3 – 7x – 6

AX3 + BX2 +CX – 3AX2 – 3BX – 3c = x3 – 7x – 6

                  A = 1

B – 3A = 0

B – 3 x 1 = 0

B = 3

-3c = -6

    c = 2

 

  1. a) 8(22)y = 6 x 2y – 1

                         let t = 2y

                        8t2 = 6t – 1

                         8t2 – 4t – 2t + 1 = 0

(4t – 1) (2t – 1) = 0

t = ¼ or ½

\t =  2y = ¼ = 2-2

\y = -2

0r   t = 2y = ½ = 2-1

\y = -1

\y = -2 0r -1

  1. b) Numerator = 2x2 – 98

                         = 2(x2 – 49)

                        = 2(x+ 7) (x -7)

  Denominator = 3x2 – 16x – 35

                       = 3x2 – 21x + 5x – 35

                       = 3x(x -7) + 5(x – 7)

                       = (x – 7) (3x + 5)

\2x2 – 98   ¸        x + 7 = 2(x + 7) (x – 7) x (3x + 5)

                          3x2 – 16x – 3    3x + 5  (3x + 5) (x – 7)     (x + 7)

                        

                                                       = 2

  1. (2x- y) (2x + y) 

             (x – 3y) (2x – y) 

              2x + y 

              x – 3y

 

  1. P2 – 2pq + q2 = (p-q)2

P3 – pq2 + p2q – q3

= p(p2-q2) + q (p2 – q2)

 = (p+ q) (p2-q2)

(p – q)2                        = (p – q)2 P

1

(p+ q) (P2 – q2)        (p+q)2 (p-q)

                                     = p- q

                                     (p + q)2

 

 

  1. Let the numbers be a and b

 a + b = 15 – x3

 5a – 3b = 19 x 1

 

            3a + 3b = 45

            5a – 3b  = 19

              8a        = 64

            a   = 8

            b = 7  

 

                             4          3          2

23.       3(2x-5) – 4(1-x) – 6(x-4)

                  12

6x – 15 – 4+ 4x – 6x + 24

                   12

4x – 5

                                       12

 

  1. 3a2 + 4ab + b2 = 3a2 + 3ab + ab +b2

4a2 + 3ab – b2      4a2 + 4ab – ab – b2

= 3a(a+b) + b(a+b)

               4a(a+b) – b(a+b)

= (3a+b) (a+b)

               (a+b) (4a-b)

= 3a + b

              4a -b




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