Question

Simplify: (3x + y)3 + (3x – y)3​

Answer 1

Answer:

6(3x+y)

Step-by-step explanation:

3(x+y)3 + (3x-y)3

9x+9y + 9x-3y

9x+9x + 9y-3y

18x + 6y

6(3x+y)

Answer 2

Answer:

( 3x + y )³ + ( 3x - y )³ = 54x² + 6y²

Step-by-step-explanation:

We have given that ( 3x + y )³ + ( 3x - y )³.

We have to simplify the given expression.

Now,

( 3x + y )³ + ( 3x - y )³

Let,

( 3x + y ) = a

( 3x - y ) = b

We know that,

a³ + b³ = ( a + b ) ( a² - ab + b² )

By using this algebraic identity, we get,

( 3x + y )³ + ( 3x - y )³

⇒ [ ( 3x + y ) + ( 3x - y ) ] [ ( 3x + y )² - ( 3x + y ) ( 3x - y ) + ( 3x - y )² ]

⇒( 3x + y + 3x - y ) [ ( 3x )² + 2 * 3x * y + ( y )² - ( 3x + y ) ( 3x - y ) + ( 3x - y )² ] .... [ ( a + b )² = a² + 2ab + b² ]

⇒ ( 3x + 3x ) [ 9x² + 6xy + y² - ( 3x )² - ( y )² + ( 3x - y )² ] .... [ ( a + b ) ( a - b ) = a² - b² ]

⇒ 6x [ 9x² + 6xy + y² - 9x² - y² + ( 3x )² - 2 * 3x * y + ( y )² ] .... [ ( a - b )² = a² - 2ab + b² ]

⇒ 6x ( 9x² + 6xy + y² - 9x² - y² + 9x² - 6xy + y² )

⇒ 6 ( 9x² - 9x² + 9x² + y² - y² + y² + 6xy - 6xy )

⇒ 6 ( 9x² + y² )

⇒ 54x² + 6y²

∴ ( 3x + y )³ + ( 3x - y )³ = 54x² + 6y²