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

1.	What must be added each of the following expression to make it a whole square?(i) 4x2 - 12x + 7(ii) 4x2 - 20x + 20
Answer» (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

What must be added each of the following expression to make it a whole square?(i) 4x2 - 12x + 7(ii) 4x2 - 20x + 20

Answer»

(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