Question

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

Answer 1

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

Answer 2

Evaluate : (4x+2y)3 = 64x3+96x2y+48xy2+8y3

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

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

128x3 + 96xy2 = 32x • (4x2 + 3y2)

Final result :

32x • (4x2 + 3y2)