Question
nake \( x \) the sabiect of fommular in \( a\left(a^{2}-x\right)-b\left(b^{2}-x\right) \)
Ask by Page Wagner. in Nigeria
Dec 02,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{a^{3}-b^{3}}{a-b} \)
Solution
To make \( x \) the subject of the formula \( a(a^{2}-x)-b(b^{2}-x) \), we need to isolate \( x \) on one side of the equation.
Given formula: \( a(a^{2}-x)-b(b^{2}-x) \)
Let's simplify the formula first:
\( a(a^{2}-x)-b(b^{2}-x) \)
\( a^{3}-ax-b^{3}+bx \)
Now, let's isolate \( x \) on one side of the equation:
\( a^{3}-ax-b^{3}+bx = 0 \)
\( a^{3}-b^{3} = ax-bx \)
\( a^{3}-b^{3} = x(a-b) \)
\( x = \frac{a^{3}-b^{3}}{a-b} \)
Therefore, the formula with \( x \) as the subject is \( x = \frac{a^{3}-b^{3}}{a-b} \).
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To make \( x \) the subject of the formula, start by expanding the equation: \[ a(a^2 - x) - b(b^2 - x) = 0 \] This simplifies to: \[ a^3 - ax - b^3 + bx = 0 \] Rearranging terms gives: \[ ax - bx = a^3 - b^3 \] Now, factor out \( x \) from the left side: \[ x(a - b) = a^3 - b^3 \] Finally, solving for \( x \) yields: \[ x = \frac{a^3 - b^3}{a - b} \] And there you have it! \( x \) is now the subject of the formula.
