simplify. (2x+y)^3 +(2x-y)^3

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07-09-2021
Mathematics

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simplify. (2x+y)^3 +(2x-y)^3

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ghaithgh ghaithgh · Answer 1 · 2021-09-07T10:29:31-04:00

ghaithgh ghaithgh

07-09-2021

Answer:

[tex] {(2x + y)}^{3} + {(2x - y)}^{3} \\ \\{(2x + y)}^{2}(2x + y)\: + (2x - y)^{2}(2x - y) \\ \\ (4 {x}^{2} + 4xy + {y}^{2} )(2x + y) + (4 {x}^{2} - 4xy + {y}^{2} )(2x - y) \\ \\ (8 {x}^{3} + 12 {x}^{2} y + 6x {y}^{2} + {y}^{3} ) + (8 {x}^{3} - 12 {x}^{2} y + 6x {y}^{2} - {y}^{3} ) \\ \\ = 16 {x}^{3} + 12x {y}^{2} [/tex]

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