Solve p*(1-2q)-(3p-1)*(-q)-(p-1)*q=

$$p \cdot ( 1 - 2 q ) - ( 3 p - 1 ) \cdot ( - q ) - ( p - 1 ) \cdot q =$$

Evaluate

$$p$$

Solution Steps

Use the distributive property to multiply p by 1-2q.

$$p-2pq-\left(3p-1\right)\left(-q\right)-\left(p-1\right)q$$

Use the distributive property to multiply 3p-1 by -q.

$$p-2pq-\left(3p\left(-q\right)-\left(-q\right)\right)-\left(p-1\right)q$$

Multiply -1 and -1 to get 1.

$$p-2pq-\left(3p\left(-q\right)+q\right)-\left(p-1\right)q$$

To find the opposite of 3p\left(-q\right)+q, find the opposite of each term.

$$p-2pq-3p\left(-q\right)-q-\left(p-1\right)q$$

Multiply -3 and -1 to get 3.

$$p-2pq+3pq-q-\left(p-1\right)q$$

Combine -2pq and 3pq to get pq.

$$p+pq-q-\left(p-1\right)q$$

Use the distributive property to multiply p-1 by q.

$$p+pq-q-\left(pq-q\right)$$

To find the opposite of pq-q, find the opposite of each term.

$$p+pq-q-pq-\left(-q\right)$$

The opposite of -q is q.

$$p+pq-q-pq+q$$

Combine pq and -pq to get 0.

$$p-q+q$$

Combine -q and q to get 0.

$$p$$

Differentiate w.r.t. p

$$1$$

Steps Using Definition of a Derivative

Use the distributive property to multiply p by 1-2q.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-2pq-\left(3p-1\right)\left(-q\right)-\left(p-1\right)q)$$

Use the distributive property to multiply 3p-1 by -q.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-2pq-\left(3p\left(-q\right)-\left(-q\right)\right)-\left(p-1\right)q)$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-2pq-\left(3p\left(-q\right)+q\right)-\left(p-1\right)q)$$

To find the opposite of 3p\left(-q\right)+q, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-2pq-3p\left(-q\right)-q-\left(p-1\right)q)$$

Multiply -3 and -1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-2pq+3pq-q-\left(p-1\right)q)$$

Combine -2pq and 3pq to get pq.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+pq-q-\left(p-1\right)q)$$

Use the distributive property to multiply p-1 by q.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+pq-q-\left(pq-q\right))$$

To find the opposite of pq-q, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+pq-q-pq-\left(-q\right))$$

The opposite of -q is q.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+pq-q-pq+q)$$

Combine pq and -pq to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-q+q)$$

Combine -q and q to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p)$$

The derivative of ax^{n} is nax^{n-1}.

$$p^{1-1}$$

Subtract 1 from 1.

$$p^{0}$$

For any term t except 0, t^{0}=1.

$$1$$