Question

Q. Simplify:
1.cube of (2a-9)-cube of (2a+9)

Answer 1

(a-b)³= a³ - 3a²b + 3ab² - b³



(a + b)³ =  a³ + 3a²b + 3ab² + b³
---------------------------------------------------------
               



(2a-9)³= (2a)³-3(2a)²(9)+3(2a)(9)²-(9)³
          = 8a³-108a²+486a-729

 (2a+9)³= (2a)³+(9)³+3(2a)²(9)+3(2a)(9)²
          = 8a³+729+108a²+486a
-------------------------------
(2a -9)³ - (2a + 9)³
= 8a³-108a²+486a-729- (8a³+729+108a²+486a)

= 8a³-108a²+486a-729-8a³-729-108a²-486a
= -216a²-1458


:)

Answer 2

Hi friend,

Here is the answer:

1) (2a-9)^3

(a-b)^3= a^3-3a^2b+3ab^2-b^3
Therefore,

= (2a-9)^3= (2a)^3-3(2a)^2(9)+3(2a)(9)^2-(9)^3
= 8a^3-108a^2+486a-729

2) (2a+9)^3

(a+b)^3=a^3+b^3+3a^2b+3ab^2
Therefore,

= (2a+9)^3= (2a)^3+(9)^3+3(2a)^2(9)+3(2a)(9)^2
= 8a^3+729+108a^2+486a

Equating both:

8a^3-108a^2+486a-729- (8a^3+729+108a^2+486a)

= 8a^3-108a^2+486a-729-8a^3-729-108a^2-
486a
= -216a^2-1458

Hope my answer helps you :)