Question

Expand 1) (a+ 2d)³, 2) (a-2d)²

Answer 1

Expand 1) (a+ 2d)³, 2) (a-2d)².

Good question,

Here is your perfect answer!

1) (a+2d)³

= a³ + (2d)³ + 3(a)(2d) (a+2d)

= a³ + 8d³ + 6ad(a+2d)

= a³ + 8d³ + 6a²d + 12ad².

2) (a-2d)²

= a² - 2(a)(2d) + (2d)²

= a² - 4ad + 4d².

Answer 2

The formula for expansion is given by :

( a + b )² = a² + b² + 2 ab

( a + b )³ = a³ + b³ + 3 ab ( a + b )

First expansion

( a + 2 d )³

Using : ( a + b )³ = a³ + b³ + 3 ab ( a + b )

⇒ a³ + ( 2 d )³ + 3.a.2 d ( a + 2 d )

⇒ a³ + 8 d³ + 6 ad ( a + 2 d )

⇒ a³ + 8 d³ + 6 a²d + 12 ad²

⇒ a³ + 6 a²d + 12 ad² + 8 d³ .

Second Expansion

( a - 2 d )²

Using ( a + b )² = a² + b² + 2 ab

⇒ a² + ( - 2 d )² + 2 × a × - 2 d

⇒ a² + 4 d²- 4 ad