Page 77 - Mathematics_Form_Two

Algebra

Engage in Activity 4.4 to explore more Example 4�24
on perfect squares quadratic equations.
Factorize a + 2 6 a + 9 .
5 25
Activity 4�4: Exploring the perfect
square expressions Solution
FOR ONLINE READING ONLY
6 9
1. Use the splitting of the middle term Write a + 2 a + = (a + ...)
2
method to factorise the expressions 5 25
x + 2 6x + 9 and x − 2 8x + 16 , (the first term in the bracket must be a)
and compare the results with the The second term in the bracket is Mathematics for Secondary Schools
identities (ab+ ) 2 and (ab− ) 2 . obtained by taking the square root of the

2. Study the nature of the middle terms constant term.
in task 1 after splitting and note any
unique features. 9 3
That is, = .
3. Use the findings from tasks 1 and 2, 25 5
and varieties of relevant sources to 2 6 9 3æ ö 2
2
study the characteristics of (ab+ ) Therefore, a 5 a + + 25 ç è a = + 5 ø ÷ .
2
and (ab− ) hence generalize your
findings. Note:

2
1. In a + 2 2ab b+ 2 = (a b+ ) , the
From Activity 4.4, it can be observed square of the sum of two quantities
that when factorising perfect square is equal to the sum of their squares
expressions, the middle term will always
split into two equal terms which reflect plus twice their product.
the 2ab part of a + 2 2ab b+ 2 and the 2 2 2
− 2ab part of a − 2 2ab b+ 2 . 2. In a − 2abb+ = (ab− ) ,the square
of the difference of two quantities
Example 4�23 is equal to the sum of their squares
minus twice their product.
Factorize x 2 6 + 9x - and write the
2
answer in the form of (x a+ ). 3. In all perfect squares, the constant
Solution term is the square of half the
x 2 6x - 9 (x += 3)(x- - 3) coefficient of the linear (middle)
term.
= (x - 3) 2
2
4. If ax +bx +c is a perfect square
Therefore, x 2 6x - 9 (x += - 3) 2 . then b = 4ac.
2

71
Student's Book Form Two

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MATHEMATIC F2 v5.indd 71