What is the product of (1 - p) and (1/2 - p) all reduced by p?

Perform Multiplication: Now we will perform the multiplication for each term. 1 * (1/2) = 1/2 1 * (-p) = -p -p * (1/2) = -p/2 -p * (-p) = p^2 So, (1 - p)(1/2 - p) = 1/2 - p - p/2 + p^2Combine Like Terms: Next, we combine like terms. 1/2 - p - p/2 + p^2 = (1/2 - p/2) - p + p^2 1/2 - p/2 = 1/4 So, (1 - p)(1/2 - p) = 1/4 - p + p^2Reduce by p: Now we need to reduce this expression by p, which means we subtract p from the expression we just found. (1/4 - p + p^2) - p = 1/4 - p + p^2 - pCombine Like Terms: Finally, we combine the like terms which are the p terms. 1/4 - p + p^2 - p = 1/4 + p^2 - 2p

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What is the product of $(1 - p)$ and $(\frac{1}{2} - p)$ all reduced by $p$ ?

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Calculus

Evaluate definite integrals using the chain rule

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Q. What is the product of

(1 - p)

and

(\frac{1}{2} - p)

all reduced by

p

Perform Multiplication: Now we will perform the multiplication for each term. $\newline$ $1 \times (\frac{1}{2}) = \frac{1}{2}$ $\newline$ $1 \times (-p) = -p$ $\newline$ $-p \times (\frac{1}{2}) = -\frac{p}{2}$ $\newline$ $-p \times (-p) = p^2$ $\newline$ So, $(1 - p)(\frac{1}{2} - p) = \frac{1}{2} - p - \frac{p}{2} + p^2$
Combine Like Terms: Next, we combine like terms. $\newline$ $\frac{1}{2} - p - \frac{p}{2} + p^2 = (\frac{1}{2} - \frac{p}{2}) - p + p^2$ $\newline$ $\frac{1}{2} - \frac{p}{2} = \frac{1}{4}$ $\newline$ So, $(1 - p)(\frac{1}{2} - p) = \frac{1}{4} - p + p^2$
Reduce by $p$ : Now we need to reduce this expression by $p$ , which means we subtract $p$ from the expression we just found. $\newline$ $(\frac{1}{4} - p + p^2) - p = \frac{1}{4} - p + p^2 - p$
Combine Like Terms: Finally, we combine the like terms which are the $p$ terms. $\frac{1}{4} - p + p^2 - p = \frac{1}{4} + p^2 - 2p$