Question

simplify (4x+2y)^3 + (4x-2y)^3​

Answer 1

hope you like that answer

Answer 2

Answer:

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