Question

Q 1.) Expand using identities:i. (a+2b)²ii. (5x-3y)²iii. (3a+4)(3a-4)(9a²+16)​

Answer 1

Step-by-step explanation:

#1.

(a + 2b)²

Using identity (x + y)² = x² + 2xy + y², we get:

= (a)² + (2b)² + 2 × (a) × (2b)

= a² + 4b² + 4ab

= a² + 4ab + 4b² Ans.

#2.

(5x - 3y)²

Using identity (a - b)² = a² - 2ab + b², we get:

= (5x)² + (3y)² - 2 × (5x) × (3y)

= 25x² + 9y² - 30xy

= 25x² - 30xy + 9y² Ans.

#3.

(3a + 4)(3a - 4)(9a² + 16)

Using identity (x + y)(x - y) = x² - y², we get:

= [(3a)² - (4)²][9a² + 16]

= (9a² - 16)(9a² + 16)

= (9a²)² - (16)²

= 81a⁴ - 256 Ans.