Worksheet on Completing Square

Practice the questions given in the worksheet on completing square.

1. Write the following as a perfect square.

(i) 4X2 + 4X + 1

(ii) 9a2 – 12ab + 4b2

(iii) 1 + 6a + 9a2

2. Indicate the perfect squares among the following. Express each of the perfect squares as the square of a binomial. What numbers should be added to those which are not perfect squares so that the expressions may become perfect squares?

(i) 36x2 – 60xy + 25y2

(ii) x2 + 4x + 1

(iii) 4a2 + 4a

(iv) 9a2 – 6a + 1

(v) 16 – 24a + 9a2

(vi) 25x2 + 10x – 1


3. Find the missing term in each of the following so that the expression becomes a perfect square.

(i) 25x2 + (..........) + 49

(ii) 64a2 - (..........) + b2

(iii) 9 + (..........) + x2

(iv) 16a2 + 8a + (..........)

(v) (..........) – 18x + 9x2

(vi) x2 – 2 + (..........)


4. Each of the following is a perfect square. Find the numerical value of k.

(i) 121a2 + ka + 1

(ii) 3ka2 + 24a + 4

[Hint: 3ka2 + 2 ∙ 6a ∙ 2 + 22. So, 3ka2 = (6a)2. Therefore, 3k = 62]

(iii) 4x4 + 12x2 + k


5. What should be added to make each of the following a perfect square?

(i) 25x2 + 81

(ii) 81x2 – 18x

(iii) a4+ 1a4

 

Answers for the worksheet on completing square are given below.

 

Answer:


1. (i) (2x + 1)2

(ii) (3a – 2b)2

(iii) (1 + 3a)2


2. (i) Perfect square, (6x – 5y)2

(ii) Not a perfect square, 3

(iii) Not a perfect square, 1

(iv) Perfect square, (3a - 1)2

(v) Perfect square, (4 – 3a)2

(vi) Not a perfect square, 2


3. (i) 70x

(ii) 16ab

(iii) 6x

(iv) 1

(v) 9

(vi) 1x2


4. (i) 22

(ii) 12

(iii) 9


5. (i) 90x

(ii) 1

(iii) 2 or -2







9th Grade Math

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