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Year 10 Interactive Maths - Second Edition


Recognition of Perfect Squares

It is useful to be able to recognise perfect squares.

When the perfect square is expanded, notice that the square of (half of the coefficient of x) is equal to the constant term.

The expression x squared + 12x + 36 is a perfect square as it can be expressed as (x + 6) squared.


Example 10

Which of the following expressions are perfect squares?

a.  x squared + 16x + 64, b.  x squared - 14x + 48

Solution:

x squared + 16x + 64 is a perfect square as the third term is (half the coefficent of x) squared.

x squared - 14x + 48 is not a perfect square as the third term is not (half the coefficent of x) 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 ]

 

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