Make h the subject of h/(4p) = p - 5k, expanding any brackets in your answer.

Step-by-step solution

1. 1

   Identify what is currently attached to h. On the left, $h$ is divided by $4p$. To free it, apply the inverse operation to both sides: multiply by $4p$.

2. 2

   Multiply both sides by 4p. Keep the whole right-hand side in brackets — this is where the second term usually gets lost:

   $h=4p\left(p-5k\right).$

3. 3

   Expand the bracket as instructed. The factor $4p$ multiplies each term inside:

   $4p\cdot p=4p^{2},\qquad 4p\cdot(-5k)=-20pk.$

4. 4

   Write the final rearranged formula.

   $h=4p^{2}-20pk.$

   Answering $4p^2-5k$ — multiplying only the first term — is the classic error the instruction 'expand any brackets' is designed to expose.

5. 5

   Check by reversing. Divide the answer by $4p$:

   $\frac{4p^{2}-20pk}{4p}=\frac{4p^{2}}{4p}-\frac{20pk}{4p}=p-5k\ \checkmark$

6. 6

   Test with numbers. Take $p=2$ and $k=1$. The original right side is $2-5=-3$, so $h$ should be $4(2)(-3)=-24$. The formula gives $4(4)-20(2)(1)=16-40=-24$ ✓.