Question

please answer this question​

Answer 1

Step-by-step explanation:

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Answer 2

The simplified form of the given expression is 2y² ( 3y + 5x²).

• The given expression is { (x / 3) + (y / 5) }³ - { (x / 3) - (y / 5) }³

Let (x / 3) be considered as a, and (y / 5) be considered as b.

• Substituting (x / 3) and (y / 5) with a and b respectively, the expression becomes,

(a + b)³ - (a - b)³

• We know that the expansion of (a + b)³ = a³ + b³ + 3ab (a + b),

and that of (a - b)³ = a³ - b³ - 3ab (a - b)

• Therefore, expanding (a + b)³ and (a - b)³ in the given expression, we get,

{ a³ + b³ + 3ab (a + b) } - { a³ - b³ - 3ab (a - b) }

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

= a³ + b³ + 3a²b + 3ab² - a³ + b³ + 3a²b - 3ab²

= 2b³ + 6a²b  -(i)

• Now, putting a as (x / 3) and b as (y / 5) in (i), we get,

{ 2 × (y / 5)³ } + { 6 × (x / 3)² × (y / 5) }

= { 2 × (y³ / 125) } + { 6 × (x² / 9) × (y² / 25) }

= ( 2y³ / 125 ) + { 6x²y² / (9 × 25) }

= (2y³ / 125) + (2x²y² / 75)

= (2y³ × 3) + (2x²y² × 5)

= 6y³ + 10x²y²

= 2y² ( 3y + 5x²)

∴ { (x / 3) + (y / 5) }³ - { (x / 3) - (y / 5) }³ = 2y² ( 3y + 5x²)