Question

Simplify: (3x - 2y)³ - (3x + 2y)³

Answer 1

3x-2y=a  3x+2y=b
The equation becomes
a³-b³
= (a-b)(a²+ab+b²)
=(3x-2y-3x-2y)[(3x-2y)²+(3x+2y)(3x-2y)+(3x+2y)²]
=-4y[2(9x²+4y²)+(9x²-4y²)]           (As (a+b)²+(a-b)²=2(a²+b²))
=-4y(18x²+8y²+9x²-4y²)
=-4y(27x²+4y²)
=-108x²-16y²

Answer 2

Answer:

$(3x - 2y)^3- (3x + 2y)^3=-108x^2-16y^2$

Step-by-step explanation:

Given : Expression $(3x - 2y)^3- (3x + 2y)^3$

To find : Simplify the given expression?

Solution :

We know, The identity $a^3-b^3= (a-b)(a^2+ab+b^2)$

On comparison with given expression

3x-2y=a  3x+2y=b

Substitute the values in the identity we get,

$(3x - 2y)^3- (3x + 2y)^3=(3x-2y-3x-2y)[(3x-2y)^2+(3x+2y)(3x-2y)+(3x+2y)^2]$

Applying, $(a+b)^2+(a-b)^2=2(a^2+b^2)$

$(3x - 2y)^3- (3x + 2y)^3=-4y[2(9x^2+4y^2)+(9x^2-4y^2)]$

$(3x - 2y)^3- (3x + 2y)^3=-4y(18x^2+8y^2+9x^2-4y^2)$

$(3x - 2y)^3- (3x + 2y)^3=-4y(27x^2+4y^2)$

$(3x - 2y)^3- (3x + 2y)^3=-108x^2-16y^2$

Therefore, The simplication is $(3x - 2y)^3- (3x + 2y)^3=-108x^2-16y^2$