Topic Content:
- Perfect Squares
- Perfect square with a + sign between the two numbers
Perfect square with a negative sign between the two numbers
Worked Examples
- Perfect square with a + sign between the two numbers
A perfect square with a + sign between the two numbers:
(x + a)2 = ( x + a) (x + a)
⇒ x (x + a) + a (x + a)
⇒ x2 + ax + ax + a2
⇒ (x + a)2 = x2 + 2ax + a2
We can state the above result as follows:
The first term squared + twice their product + the square of the second term.
A perfect square with a negative sign between the two numbers:
(x – a)2 = (x – a) (x – a)
⇒ x(x – a) – a (x – a)
⇒ x2 – ax – ax – a2
⇒ x2 – 2ax – a2
⇒ (x – a)2 = x2 – 2ax + a2.
We can state the above result as follows:
the first term squared – twice their product + the square of the second term.
Worked Example 7.1.1:
Write down the expansions of the following:
a. (y + 8)2
b. (y – 5)2
c. (7a – 3)2
d. (2y – 6)2
e. (5x + 4y)2
Solution
a. (y + 8)2
⇒ (y + 8) (y + 8)
⇒ y (y + 8) + 8 (y + 8)
⇒ y2 + 8y + 8y + 64
= y2 + 16y + 64
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