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"Question 2 Use the identity (x + a) (x + b) = x^2 + (a + b)x + ab to find the following products. (i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1) (iii) (4x − 5) (4x − 1) (iv) (4x + 5) (4x − 1) (v) (2x +5y) (2x + 3y) (vi) (2a^2 +9) (2a^2 + 5) (vii) (xyz − 4) (xyz − 2)

Class 8 Algebraic Expressions and Identities Page 151"

Answers

Answered by nikitasingh79
37

An identity is true only for certain values of its variables. An equation is not an identity.

The following are the identities

(a + b)² = a² + 2ab + b² 
(a – b)
² = a² – 2ab + b² 
(a – b)(a + b) = a
² – b²

 Another useful identity is

 (x + a) (x + b) = x² + (a + b) x + ab

If the given expression is the difference of two squares we use the formula

a² –b² = (a+b)(a-b)

 

• The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.

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Solution:

1) (x + 3) (x + 7)

x² + (3+7)x + 21


= x² + 10x + 21

 


2)  (4x + 5) (4x + 1)

(4x + 5) (4x + 1)

= 16x² + (5 + 1)4x + 5

= 16x² + 24x + 5

 


3) (4x – 5) (4x – 1)


= 16x²+ (-5-1)4x + 5


= 16x² - 24x + 5


4) (4x + 5) (4x – 1)


= 16x²+ (5-1)4x - 5


= 16x² +16x – 5


5) (2x + 5y) (2x + 3y)
= 4x² + (5y + 3y)2x + (5y×3y)

=4x² + (8y)2x + 15y²


= 4x² + 16xy + 15y²


6) (2a²+ 9) (2a²+ 5)
= 4a⁴ + (9+5)2a² + 9×5

=4a⁴ + (14)2a² + 9×5

= 4a⁴ + 28a² + 45


7) (xyz – 4) (xyz – 2)

(xyz)²+(-4-2)xyz+ (-4×-2)
= x²y²z² + (-6)xyz + 8


= x²y²z² - 6xyz + 8

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Hope this will help you.....

Answered by mariasweetie2002
4

Answer:

Hey mate your answer is here.

Step-by-step explanation:

(i) (x + 3) (x + 7)

= x² + (3+7)x + 21

= x²+ 10x + 21

ii) (4x + 5) (4x + 1)

= 16x2 + (5 + 1)4x + 5

=  + 24x + 5

iii) (4x – 5) (4x – 1)

= 16x2 – 4x – 20x + 5

= 16x2 – 24x + 5

iv) (4x + 5) (4x – 1)

= 16x2 + (5-1)4x – 5

= 16x2 +16x – 5

v) (2x + 5y) (2x + 3y)

= 4x2 + (5y + 3y)2x + 15y2

= 4x2 + 16xy + 15y2

vi) (2a2+ 9) (2a2+ 5)

= 4a4 + (9+5)2a2 + 45

= 4a4 + 28a2 + 45

vii) (xyz – 4) (xyz – 2)

= x2y2z2 + (-4 -2)xyz + 8

= x2y2z2 – 6xyz + 8

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