Completing Quadratic Expressions into Perfect square

Examples of perfect squares include (i) x² + 2x + 1,       x² – 6x + 9,    4x²– 4x + 1 etc.

Example: Find the term when added will change the expression x² + 4x into perfect square.

Solution

Let the constant term be n

X² + 4x + n = (x + a)²

X² + 4x + n = x² + 2ax + a²

2a = 4

a = 2

n = a²

n = 2² = 4

OR

Step 1: Find half the coefficient of x i.e  2

Step 2: square this result i.e 2² = 4

Step 3: add this square to the original expression to obtain a perfect square.  X² + 4x + 4

Exercise:

Change the following expressions into a perfect square

1. 2x² – 3x         3x² – 2m      c.         2v² – 5v         d.        2x² + x     e.         5x² + 4x          f.         3x² – 10x