Subtract :
`3p^(3)-5p^(2)q` from `q^(2)+p^(2)q-4p^(3)`

Answer

To solve the problem of subtracting \(3p^{3} - 5p^{2}q\) from \(q^{2} + p^{2}q - 4p^{3}\), we will follow these steps:

### Step 1: Write down the expressions
We have two algebraic expressions:
1. \(A = q^{2} + p^{2}q - 4p^{3}\)
2. \(B = 3p^{3} - 5p^{2}q\)

We need to perform the operation \(A - B\).

### Step 2: Substitute the expressions into the subtraction
Now we will substitute \(A\) and \(B\) into the subtraction:
\[ A - B = (q^{2} + p^{2}q - 4p^{3}) - (3p^{3} - 5p^{2}q) \]

### Step 3: Distribute the negative sign
Distributing the negative sign across the second expression:
\[ A - B = q^{2} + p^{2}q - 4p^{3} - 3p^{3} + 5p^{2}q \]

### Step 4: Combine like terms
Now we will combine the like terms:
- The \(q^{2}\) term remains as is: \(q^{2}\)
- For the \(p^{2}q\) terms: \(p^{2}q + 5p^{2}q = 6p^{2}q\)
- For the \(p^{3}\) terms: \(-4p^{3} - 3p^{3} = -7p^{3}\)

Putting it all together, we have:
\[ A - B = q^{2} + 6p^{2}q - 7p^{3} \]

### Final Answer
Thus, the result of subtracting \(3p^{3} - 5p^{2}q\) from \(q^{2} + p^{2}q - 4p^{3}\) is:
\[ q^{2} + 6p^{2}q - 7p^{3} \]

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