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

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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

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Question: 8

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Question: 9

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Question: 10

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

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Question: 11

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

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Question: 12

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

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Question: 13

Find the values of the following expressions

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Question: 14

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Question: 15

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Question: 16

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

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Question: 17

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

(i) x + y

(ii) x – y

(iii) x⁴ + y⁴

Solution: