Question

simplify= (4x+y)³+(4x-2y)³

Answer 1

Instead of opening the brackets by using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we will use the identity, a³ + b³ = (a + b)(a² + b² - ab)

So,

(4x + y)³ + (4x - 2y)³

= (4x + y + 4x - 2y)[(4x + y)² + (4x - 2y)² - (4x + y)(4x - 2y)]

=> (8x - y)[ 16x² + y² + 8xy + 16x² + 4y² - 16xy - (16x² - 8xy + 4xy - 2y²)]

=> (8x - y)(32x² + 5y² - 8xy - 16x² + 8xy - 4xy + 2y²)

=> (8x - y)(16x² + 7y² - 4xy)

Now just open the brackets

=> 128x³ + 56xy² - 32x²y - 16x²y - 7y³ + 4xy²

Further solving,

=> 128x³ - 7y³ + 60xy² - 48x²y

Hope it helps dear friend ☺️

Answer 2

here is our answer 1.1 Evaluate : (4x+2y)3 = 64x3+96x2y+48xy2+8y3
1.2 Evaluate : (4x-2y)3 = 64x3-96x2y+48xy2-8y3

128x3 + 96xy2 = 32x • (4x2 + 3y2

results is 32x • (4x2 + 3y2)

hope you get your answer

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