Question

Expand each of the following, using suitable identities: i) (2x-y)²
ii) (3x + 5)² - ²
iii) (x - 1/3 ) ²
iv) (4x + 5) (4x - 5)
v) (2x + 3) (2x-3)​

Answer 1

Answer:

i) (2x-y)² = 4x² - 4xy + y²

ii) (3x + 5)²= 9x² + 30x + 25

iii) (x - 1/3 ) ² = x² - 2/3x + 1/9

iv) (4x + 5) (4x - 5) = 16x² - 25

v) (2x + 3) (2x-3) = 4x² - 9

Step-by-step explanation:

(i) :-

= (2x-y)²

= *(a-b)² = a² - 2ab + b²*

= (2x-y)² = (2x)² - 2(2x)(y) + (y)²

= (2x-y)² = 4x² - 4xy + y² (Answer)

(ii) :-

= (3x + 5)²

= *(a+b)² = a² + 2ab + b²*

= (3x + 5)²= (3x)² + 2(3x)(5) + (5)²

= (3x + 5)²= 9x² + 30x + 25 (Answer)

(iii) :-

= (x - 1/3 ) ²

= *(a-b)² = a² - 2ab + b²*

= (x - 1/3 ) ² = (x)² - 2(x)(1/3) + (1/3)²

= (x - 1/3 ) ² = x² - 2/3x + 1/9 (Answer)

(iv) :-

= (4x + 5) (4x - 5)

= *(a+b) (a-b) = a² - b²*

= (4x + 5) (4x - 5) = (4x)² - (5)²

= (4x + 5) (4x - 5) = 16x² - 25 (Answer)

(v) :-

= (2x + 3) (2x-3)

= *(a+b) (a-b) = a² - b²*

= (2x + 3) (2x-3) = (2x)² - (3)²

= (2x + 3) (2x-3) = 4x² - 9 (Answer)