Page 76 - Mathematics_Form_Two

Algebra

11. The area of a rectangular floor Example 4�20
is defined by the expression Factorize a 2 25b - 2 .
(4t +5t +1) square metre. Use this
2
expression to express the possible Solution
dimensions of the floor. Write a 2 25b - 2 as a difference of two
squares. 2 a = 2 5 b- 2 2
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12. John is trying to simplify the
Mathematics for Secondary Schools how to distribute his resources more a 2 (a= 2 2 - 25b = ) (a - 5 )(ba + 5b ).
2
a
25b -
2
expression −1 + x +2x to determine
2
2
a =
25b -
(5b-

5)b
5)(ba +
efficiently. To help him, factorize
2
Therefore, a -
the expression to better understand
the optimal allocation.
2
Factorization by the difference of two Example 4�21 81.
Factorize x -
squares Solution

2
2
An expression in the form a − b is Write x - 81 as a difference of two
2
called the difference of two squares. squares. That is,
Engage in Activity 4.3 to explore more x 2 81 x - = 2 - 9 2
about quadratic expressions which exist (x = 9)(x + - 9)
as a difference of two squares. Therefore, x 2 81 (x - = 9)(x + - 9).
Example 4�22
Activity 4.3: Exploring the difference
2
of two squares Find the exact value of 50001 − 49999 2
1. Determine the product of (ab+ ) Solution 2
2
and (ab− ) with the identities 50001 − 49999
2
2
a − b and give your conclusion. = (50001 + 49999) (50001 − 49999)
= 100000 × 2
2. Use the results in task 1 to simplify = 200000
the expression of the form ()ax − b 2 2 2
2

and note down your observations. Therefore, 50001 − 49999 = 200000.
3. Use numbers and letters to create Factorization of perfect squares
other similar expressions. A quadratic expression whose factor are
identical is called a perfect square.
4. Confirm your findings by consulting Consider a + 2 2ab b+ 2 = (a b+ )
2
other relevant sources such as books
2
and the internet and share your and a − 2 2abb+ 2 = (ab− ). The two
findings. quadratic identities, (ab+ ) 2 and (ab− ) 2

are called perfect squares.

70
Student's Book Form Two

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MATHEMATIC F2 v5.indd 70
MATHEMATIC F2 v5.indd 70 11/10/2024 20:11:55