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Simplify: (3x+y)³ − (3x − y )³
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Please Answer this question
Simplify: (3x+y)³ − (3x − y )³
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Step-by-step explanation:
To simplify the expression (3x+y)³ - (3x-y)³, we can use the formula for the difference of cubes, which states that a³ - b³ = (a - b)(a² + ab + b²).
In this case, let's label (3x+y) as a and (3x-y) as b.
So, we have: (3x+y)³ - (3x-y)³ = (a - b)(a² + ab + b²).
Plugging in the values: (3x+y - (3x-y))((3x+y)² + (3x+y)(3x-y) + (3x-y)²).
Simplifying further:
(2y)(9x² + 6xy + y² + 9x² - 6xy + y²) = 2y(18x² + 2y²).
So, the simplified expression is 2y(18x² + 2y²).
Answer:
2y[tex]^{3}[/tex] or 2y*2y*2y