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G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

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.

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