Make x subject of formula in: a(a(a)-x)=b(b(b)-x)

Answer 1

To make x the subject of the formula, we need to isolate x on one side of the equation. Let's simplify the given equation step-by-step:

a(a(a) - x) = b(b(b) - x)

Expand the brackets:

a(a^2 - ax) = b(b^2 - bx)

Multiply the terms inside the brackets:

a(a^2 - ax) = b(b^2 - bx)
a^3 - a^2x = b^3 - b^2x

Rearrange the terms and collect the x terms on the left side:

a^3 + b^2x - a^2x = b^3

Now, let's group the x terms:

(b^2 - a^2)x = b^3 - a^3

Divide both sides by (b^2 - a^2) to isolate x:

x = (b^3 - a^3)/(b^2 - a^2)

Therefore, x is the subject of the formula:
x = (b^3 - a^3)/(b^2 - a^2)

Answer 2

wrong again!
a(a(a) - x) = b(b(b) - x)
a^3 - ax = b^3 - bx
bx-ax = b^3-a^3
(b-a)x = b^3-a^3 = (b-a)(b^2+ab+a^2)
x = b^2+ab+a^2

Answer 3

Apologies for the mistake in my previous response. Here is the correct solution:

Given equation: a(a(a) - x) = b(b(b) - x)

Expanding the brackets:
a^3 - ax = b^3 - bx

Rearranging the terms and collecting the x terms on the right side:
bx - ax = b^3 - a^3

Factoring out (b - a) from both terms:
(b - a)x = b^3 - a^3

Dividing both sides by (b - a) to isolate x:
x = (b^3 - a^3)/(b - a)

Now, applying the factorization formula for the difference of cubes (a^3 - b^3 = (a - b)(a^2 + ab + b^2)), we can simplify the expression:

x = (b^3 - a^3)/(b - a) = ((b - a)(b^2 + ab + a^2))/(b - a)

The (b - a) terms cancel out, leaving us with:

x = b^2 + ab + a^2

Thus, the correct solution is x = b^2 + ab + a^2.