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If
p=-3 and
q=5, find the value of
p^(2)-q^(2)p-p^(3).

If $p=-3$ and $q=5$ , find the value of $p^{2}-q^{2} p-p^{3}$ .

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Evaluate expression when two complex numbers are given

Full solution

Q. If

p=-3

and

q=5

, find the value of

p^{2}-q^{2} p-p^{3}

.

Given Values: We are given: $\newline$ $p = -3$ $\newline$ $q = 5$ $\newline$ Expression = $p^{2} - q^{2}p - p^{3}$ $\newline$ Identify the expression after substituting the values of $p$ and $q$ . $\newline$ Substitute $-3$ for $p$ and $5$ for $q$ in $p^{2} - q^{2}p - p^{3}$ . $\newline$ $q = 5$ $0$
Calculate $p^2$ : Calculate $p^2$ which is $(-3)^2$ . $\newline$ $(-3)^2 = 3 \times 3$ $\newline$ $= 9$
Calculate $q^2$ : Calculate $q^2$ which is $(5)^2$ . $\$5$ ^ $2$ = $5$ \times $5$ = $25$ \)
Multiply $q^{2}$ by $p$ : Multiply $q^{2}$ by $p$ which is $25 \times (-3)$ . $\newline$ $25 \times (-3) = -75$
Calculate $p^{3}$ : Calculate $p^{3}$ which is $(-3)^{3}$ . $\newline$ $(-3)^{3}$ = $-3 \times -3 \times -3$ $\newline$ = $-27$
Combine Calculated Parts: Combine all the calculated parts to find the value of the expression. $\newline$ $p^{2} - q^{2}p - p^{3} = 9 - (-75) - (-27)$
Simplify the Expression: Simplify the expression by performing the subtractions. $9 - (-75) - (-27) = 9 + 75 + 27 = 111$

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