Algebraic Expression Questions and Answers
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Algebraic expressions
- Simplify (3mks)
- 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
- 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?
- Simplify;
(a) 6a – 2b + 7a – 4b + 2
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(b) 2x – 2 3x + 2
2x 4x
- Simplify 6x2y2 + 13xy-5
3x2y2 – 13xy + 4
- 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
- Simplify the expression.
6x2 + 35x – 6
2x2 – 72
- Simplify the expression
2/3 (3x -2) – ¾ (2x -2)
- Simplify by factorizing completely:
4y2 – x2
2x2 – yx -6y2
- Simplify as far as possible.
3 – 1
x – y x + y
- By calculation, find the coordinates of the intersection of the graphs y = x2 + 2x -5
and y = 3x +1
- Simplify:
(a) y2 + 2y = ¼
y3 – y2 – 6y
(b) hence solve:- y2 + 2y = ¼
y3 – y2 – 6y
- 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.
- Factorize completely the expression
75x2 – 27y2
- 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
- Simplify P3 –Pq2 + P2q – q3
P2 + 2pq + q2
- Simplify the expression:- 9x2 – 4y2
12x2 + yx – 6y2
- Given that (x-3) (Ax²+bx+c) = x³-7x-6, find the value of A, B and C
- a) solve for y in 8x(2²)ʸ=6×2ʸ-1
- b) Simplify completely 2x²-98 ÷ x+7
3x²-16x-35 3x+5
- Simplify the expression.:
4x2 – y2
2x2 – 7xy + 3y2
- Simplify P2 -2Pq + q2
P3 –Pq2+ P2q – q3
- 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
- Simplify the following expressions by reducing it to a single fraction
2x – 5 – 1 – x – x – 4
4 3 2
- Simplify the expression:- 3a2 + 4ab + b2
4a2 + 3ab – b2
ANSWERS for Algebraic Expression
- 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
- B.P = 160 x 50 = 24000
S.P = ((160 x 8) – (20 + 12)) x 180
8
= 28080
Profit = 28080 – 24000 = Shs.4080
- a) 6a + 7a – 2b – 4b + 2
= 13a – 6b + 2
- b) 2x – 2 – 3x + 2 = 2(2x – 2) – (3x + 2)
2x 4x 4x
= 4x – 3x – 4 – 2
4x
= x – 6
4x
- 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
- 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
- b) 2xy = 2 x 3 x 5 = 30
- c) x2 – 2xy + y2 = 9 – 2 x 3 x 5 + 25 = 4
- 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
- 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)
- 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
- 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
- 3(x + y) – (x –y)
X 2 – y2
= 3x + 3y – x + y
x2 – y2
= 2(x +2y)
x2 -y2
- 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)
- (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
- 104.6 = 44 x 2
2.4
63.9 = 26 x 2
2.4
= 88 + 54= 142
- 3 ( 25 x2 – 9y2)
3 (5x + 3y) (5x – 3y)
- i) d = 8.4 r = ½
6th jump = 8( ½ )6-1
8.4/32
= 0.2625 = 0.26cm
- ii) 56 = 4 (1 – ( ½ ) 6
1 – ½
= 8.4 x 63 x 2
64
= 16.54 cm
- 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
- ( 3x + 2y ) ( 3x – 2y )
( 3x + 2y ) ( 3x – 2y )
3x + 2y
4x + 3y
- (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
- 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
- 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
- (2x- y) (2x + y) √
(x – 3y) (2x – y) √
2x + y √
x – 3y
- 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
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(p+ q) (P2 – q2) (p+q)2 (p-q)
= p- q
(p + q)2
- 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
- 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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