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Chapter 6: Algebraic Expressions and Identities Exercise – 6.6

Question: 1

Write the following squares of binomials as trinomials

We know that, (a + b)2 = a2 + 2ab + b2 and (a – b)2 = a2 – 2ab + b2

(i) (x + 2)2

(ii) (8a + 3b)2

(iii) (2m + 1)2

Solution:

 

Question: 2

Find the product of the following binomials

(i) (2x + y) (2x + y)

(ii) (a + 2b) (a – 2b)

(iii) (a2 + bc) – (a2 – bc)

(vi) (2a3 + b3) (2a3 – b3)

Solution:

 

Question: 3

Using the formula for squaring a binomial, evaluate the following

(i) (102)2

(ii) (99)2

(iii) (1001)2

(iv) (999)2

(v) (703)2

Solution:

 

Question: 4

Simplify the following using the formula:  (a + b) (a – b) = a2 – b2

(i) (82)2 – (18)2

(ii) (467)2 – (33)2

(iii) (79)2 – (69)2

(iv) 197 × 203

(v) 113 × 87

(vi) 95 × 105

(vii) 1.8 × 2.2

(viii) 9.8 × 10.2

Solution:

 

Question: 5

Simplify the following using identities

Solution:

 

Question: 6

Find the value of x, if:

(i) 4x = (52)2 – (48)2

(ii) 14x = (47)2 – (33)2

(iii) 5x = (50)2 – (40)2

Solution:

 

Question: 7

Solution:

 

Question: 8

Solution:

 

Question: 9

Solution:

 

Question: 10

If x + y = 4 and xy = 2, find the value of x2 + y2

Solution:

 

Question: 11

If x – y = 7 and xy = 9, find the value of x2 + y2

Solution:

 

Question: 12

If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2

Solution:

 

Question: 13

Find the values of the following expressions

Solution:

 

Question: 14

Solution:

 

Question: 15

Solution:

 

Question: 16

If 2x + 3y = 14 and 2x – 3y = 2, find the value of xy

Solution:

 

Question: 17

If x2 + y2 = 29 and xy = 2, Find the value of

(i) x + y

(ii) x – y

(iii) x4 + y4

Solution:


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