Question

factories the equation(x+y)^3 -(x-y)^3​

Answer 1

..Question..

☯︎ Factorise the equation :

➪ ( x + y )³ - ( x - y )³

..Answer..

Let ,

ㅤㅤ➪ ( x + y )³ = a ------------ [( 1 )]

ㅤㅤ➪ ( x - y )³ = b ------------ [( 2 )]

•°• The equation becomes ➪ a³ - b³

➪ We know that

➪ a³ - b³ = ( a - b ) ( a² + 2ab + b² )

ㅤㅤㅤㅤ•°• A/Q

➪ ( x + y )³ - ( x - y )³

➪ ㅤㅤa³ - b³ ㅤㅤㅤ[ from ( 1 ) & ( 2 )]

➪ ( a - b ) ( a² + 2ab + b²)

➪ { ( x + y ) - ( x - y ) } { ( x + y )² + 2 ( x + y ) ( x - y ) + ( x - y )² }

➪ { x + y - x + y } { ( x² + 2xy + y² ) + ( 2x + 2y ) ( x - y ) + ( x² - 2xy + y² ) }

➪ 2y { ( x² + 2xy + y² ) + 2x ( x - y ) + 2y ( x - y ) + ( x² - 2xy + y² ) }

➪ 2y { ( x² + 2xy + y² ) + 2x² - 2xy + 2xy - 2y² + ( x² - 2xy + y² ) }

➪ 2y { x² + 2xy + y² + 2x² - 2y² + x² - 2xy + y² }

➪ 2y ( x² + x² + y² + y² + 2x² - 2y² )

➪ 2y ( 2x² + 2y² + 2x² - 2y² )

➪ 4x²y + 4y³ + 4x²y - 4y³

➪ 8x²y + 4y³ - 4y³

➪ 8x²yㅤㅤㅤㅤㅤㅤAns....

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂

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