Back to Course

SS1: MATHEMATICS - 2ND TERM

0% Complete
0/0 Steps



Lesson Progress
0% Complete

Topic Content:

  • Factorization of Perfect Squares

Expressions such as (x + y)2 and (x – y)2 are examples of perfect squares.

If we expand (x + y)2, we obtain (x + y)2 = (x + y)(x + y)

= x2 + xy + xy + y2

= x2 + 2xy + y2

The result of this equation may be stated as follows:

(1st term)2 + twice the product of the first term and the 2nd term + (2nd term)2

Similarly, if we expand (x – y)2, we obtain

(x – y)2 = (x – y)(x + y)

=x2 – xy – xy + y2

=x2 – 2xy + y2

The result is also:

(1st term)2 – twice the product of the first term and the 2nd term + (2nd term)2

It is important to know that expressions of the form x2 + 2xy + y2 and x2 – 2xy + y2 are also known as perfect squares.

Example 6.4.1:

Factorise the following:

(a) \( \scriptsize 16 \: – \: 8x \: + \: x^2 \)
(b) \( \scriptsize 4x^2 \: + \: 36x \: + \: 81 \)
(c) \( \scriptsize 1 \: – \: \normalsize \frac {2x}{3} \: + \: \frac {x^2}{9} \)
(d) \( \scriptsize 16x^2 \: – \: 64xy \: + \: 64y^2 \)

Solution

(a) \( \scriptsize 16 \: – \: 8x \: + \: x^2 \)

Rewrite as;

\( \scriptsize x^2 \: – \: 8x \: + \: 16 \)

 

You are viewing an excerpt of this Topic. Subscribe Now to get Full Access to ALL this Subject's Topics and Quizzes for this Term!

Click on the button "Subscribe Now" below for Full Access!

Subscribe Now

Note: If you have Already Subscribed and you are seeing this message, it means you are logged out. Please Log In using the Login Button Below to Carry on Studying!

avatar

Responses

Your email address will not be published. Required fields are marked *

error: Alert: Content selection is disabled!!