Question

expansion expansion expansion expansion ​

Answer 1

Answer:

The answers are 990 and 28 .

Step-by-step explanation:

The explanations are in the above attachment.

Answer 2

Answer:

1) 999

2) 28

Step-by-step explanation:

1) If a - b = 9, ab = 10, find a³ - b³

We know that

( a - b)³ = a³ - b³ - 3ab(a + b)

Substituting the given values

9³ = a³ - b³ - 3( 10 )( 9 )

729 = a³ - b³ - 270

a³ - b³ = 729 + 270 = 999

Therefore the value of a³ - b³ is 999.

2) If x + 3/x = 4, find x³ + 27/x³.

Given :

x + 3/x = 4

Cubing on both sides

( x + 3/x )³ = 4³

Using algebraic identity (a + b)³ = a³ + b³ + 3ab( a + b)

x³ + ( 3/x )³ + 3( x )( 3/x )( x + 3/x ) = 64

Using Laws of exponents ( a/b)^m = a^m / b^m

x³ + 3³/x³ + 9( 4 ) = 64

x³ + 27/x³ + 36 = 64

x³ + 27/x³ = 64 - 36

x³ + 27/x³ = 28

Therefore the value of x³ + 27/x³ is 28