Page 73 - Mathematics_Form_Two

Algebra

Note that, from the general quadratic 7. (ab− ) 2
2
expression ax + bx , c + where a, b and c (4x−3)(2x−1)
are real numbers. 8.

(a) If a = 0, the expression becomes 9. (3p + 2q )(6p − 2q )
FOR ONLINE READING ONLY
linear. For example, 6x + 4,in this 10. (x + yx ) y
)( −
case, a = 0, b = and c = 4.
6
11. (x + 2)(y − 3)
0
(b) If b = , the expression is a
quadratic but without the middle 12. ( 3 y y−+ )( + ) 4
term. For example, 4x + , in this Mathematics for Secondary Schools
2
8
case, a = 4, b = and c = 8. 13. Find the area of a triangle whose base
0
is (6x + 1) cm and height is (4x – 2)
0
(c) If c = , the expression is a cm. Write the answer in the expanded
quadratic but without the constant form.
term. For example, 10x 2 2x - , in 14. Find the amount of money required
this case, a = 10, b = − and c = 0. to buy 7y items if each item costs
2
(6y + 5) shillings. Give the answer in
(d) The basic identities of quadratic
expressions are as follows: the expanded form.

(i) (a b+ ) = 2 a + 2 2ab b+ 2 15. Given three consecutive whole
numbers, write the expanded form of
(ii) a − 2 b = 2 (a ba b+ )( − ) the product of the first and the third if
the second number is n.
(iii) (x a+ )(x b+ ) x= 2 + (a b+ )x ab+ 16. Simplify

(4a − 6)(2a + 5) (2a− + 5)(4a − 3).
Exercise 4�3 17. The width of a rectangular field is 20
In questions 1 to 12, write the expanded m shorter than its length y metres.

form of each of the given expressions: Write down an expression for the
area A.
1. (2x + 3 )(x + ) 1 18. A rope which is 42 cm long is divided

2. (4x − 32x + )( ) 1 into two pieces to make two squares.
Write an expression for the sum of
3. ( yy + ) 6 the areas.
19. A neighbour has a picture which
4. (3y + ) 4 2 measures 10 cm by 20 cm. He wants
to make a frame of constant width
5. (7n − ) 2 2 which will enclose the picture. Write

6. (ab+ ) 2 an expression for the area of the
frame.

67
Student's Book Form Two

11/10/2024 20:11:52
MATHEMATIC F2 v5.indd 67 11/10/2024 20:11:52
MATHEMATIC F2 v5.indd 67