Question

What must be added each of the following expression to make it a whole square?

(i) 4x² - 12x + 7

(ii) 4x² - 20x + 20

Answer 1

(i) 4x² - 12x + 7

(2x)² – 2 (2x) (3) + 3² – 3² + 7 

= (2x – 3)² – 9 + 7

= (2x – 3)² – 2

Hence, 2 must be added to the expression in order to make a whole square

(ii) 4x² - 20x + 20

(2x)² – 2 (2x) (5) + 5² – 5² + 20 

= (2x – 5)² – 25 + 20

= (2x – 5)² – 5

Hence, 5 must be added to the expression in order to make it a whole square