G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" available from mathssoftware.co.nz

Order Maths Software for $25

 

Year 10 Interactive Maths - Second Edition


Forming a Perfect Square

(x + 5) squared = x squared + 10x + 25

Clearly, the third term is (half the coefficent of x) squared.

So, to make x squared + 10x a perfect square, add (half the coefficent of x) squared.

In general:

To make x squared + px a perfect square, add (half the coefficent of x) squared.


Example 11

What number should be added to make the following a perfect square?

a.  x squared + 18x + ...  , b.  x squared - 20x + ...

Solution:

Half the coefficent of x is 9 and the square of 9 is 81.  So add 81.

Note:

x squared + 18x + 81 = (x + 9) squared

Half the coefficent of x is -10 and the square of -10 is 100.  So add 100.

Note:

x squared - 20x + 100 = (x - 10) squared

 

Study Another Topic in Chapter 1: Algebraic Expressions

Expressions ] Multiplication ] The Distributive Law ] Binomials ] Difference of Two Squares ] Expanding Three Terms ] Perfect Squares ] Recognition of Perfect Squares ] [ Forming a Perfect Square ] Problem Solving ] Problem Solving Unit ] Symbols ] Index ]

 

Study Another Chapter
 

| Home Page | Order Maths Software | About the Series | Maths Software Tutorials

| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software |

| Year 10 Maths Software | Homework Software | Tutor Software | Maths Software Platform |
| Trial Maths Software | Feedback | Year 7 Maths Reading | Year 8 Maths Reading |

| Year 9 Maths Reading | Year 10 Maths Reading | About mathsteacher.com |

| Our Policies | Terms and Conditions | Links | Contact |

 

The following international Websites are available for faster software downloads:
www.mathsteacher.com.au for Australia, www.mathsoftware.biz for the USA,
www.mathematicssoftware.co.uk for the UK, www.mathssoftware.co.za for South Africa
and www.mathsoftware.in for India.

 

Copyright © 2000-2011 mathsteacher.com Pty Ltd.  All rights reserved.

Australian Business Number 53 056 217 611

 

Copyright instructions for educational institutions

 

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.

If you experience difficulties when using this Website, tell us through the feedback form or by
phoning one of our contact telephone numbers.