Question

simplify.....(4x + 2y)^3 - (4x - 2y)^3

Answer 1

Step-by-step explanation:

In simplifying (4x+2y)3 - (4x-2y)3, we can use:

(a+b)³=a³+3a²b+3ab²+b³

and

(a-b)³=a³-3a²b+3ab²-b³

So,

(a+b)³  - (a-b)³  = a³+3a²b+3ab²+b³ - (a³-3a²b+3ab²-b³)

Open the bracket

(a+b)³  - (a-b)³   = a³+3a²b+3ab²+b³ - a³+3a²b-3ab²+b³

Collect the like terms

(a+b)³  - (a-b)³   = a³ - a³ + 3a²b + 3a²b + 3ab² - 3ab² + b³ + b³

                       = 3a²b + 3a²b+ b³ + b³

                       = 6a²b + 2 b³

(4x+2y)3 - (4x-2y)3

Putting a = 4x and b = 2y

(4x+2y)3 - (4x-2y)3 = 6a²b + 2 b³

                           = 6(4x)^2(2y) + 2(2y)^3

                          = 192x^2y + 16y^3

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