Evaluate Using the Given Value p^2q^2+pq-q^3-p^3 for p=0.5 and q=-0.5

$p^{2} q^{2} + p q - q^{3} - p^{3}$ for $p = 0.5$ and $q = - 0.5$

Step 1

Replace the variable $p$ with $0.5$ in the expression.

${(0.5)}^{2} q^{2} + (0.5) \cdot q - q^{3} - {(0.5)}^{3}$

Step 2

Replace the variable $q$ with $- 0.5$ in the expression.

${(0.5)}^{2} {(- 0.5)}^{2} + (0.5) \cdot (- 0.5) - {(- 0.5)}^{3} - {(0.5)}^{3}$

Step 3

Simplify each term.

Raise $0.5$ to the power of $2$ .

$0.25 {(- 0.5)}^{2} + (0.5) \cdot (- 0.5) - {(- 0.5)}^{3} - {(0.5)}^{3}$

Raise $- 0.5$ to the power of $2$ .

$0.25 \cdot 0.25 + (0.5) \cdot (- 0.5) - {(- 0.5)}^{3} - {(0.5)}^{3}$

Multiply $0.25$ by $0.25$ .

$0.0625 + (0.5) \cdot (- 0.5) - {(- 0.5)}^{3} - {(0.5)}^{3}$

Multiply $0.5$ by $- 0.5$ .

$0.0625 - 0.25 - {(- 0.5)}^{3} - {(0.5)}^{3}$

Raise $- 0.5$ to the power of $3$ .

$0.0625 - 0.25 - - 0.125 - {(0.5)}^{3}$

Multiply $- 1$ by $- 0.125$ .

$0.0625 - 0.25 + 0.125 - {(0.5)}^{3}$

Raise $0.5$ to the power of $3$ .

$0.0625 - 0.25 + 0.125 - 1 \cdot 0.125$

Multiply $- 1$ by $0.125$ .

$0.0625 - 0.25 + 0.125 - 0.125$

Step 4

Simplify by adding and subtracting.

Subtract $0.25$ from $0.0625$ .

$- 0.1875 + 0.125 - 0.125$

Add $- 0.1875$ and $0.125$ .

$- 0.0625 - 0.125$

Subtract $0.125$ from $- 0.0625$ .

$- 0.1875$