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

Multiply binomials: First, we need to multiply the two binomials (1-p) and (1/2-p) together. (1-p)(1/2-p) = 1*(1/2-p) - p*(1/2-p)Distribute terms: Now, distribute the terms within the parentheses. 1*(1/2-p) - p*(1/2-p) = 1/2 - p - (p/2) + p^2Combine like terms: Combine like terms. 1/2 - p - p/2 + p^2 = 1/2 - 3p/2 + p^2Reduce expression by P: Now, we need to reduce this expression by P, which means we subtract P from the expression we obtained. (1/2 - 3p/2 + p^2) - PSubtract P: Subtract P from the expression. (1/2 - 3p/2 + p^2) - P = 1/2 - 3p/2 + p^2 - PCombine like terms with P: Combine P with the like terms, noting that P is the same as 1*P or p/1. 1/2 - 3p/2 + p^2 - p/1 = 1/2 - 5p/2 + p^2Final simplified expression: The final simplified expression is: 1/2 - 5p/2 + p^2

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What is the product of $(1-p)$ and $\left(\frac{1}{2}-p\right)$ , 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

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

, all reduced by

P

Multiply binomials: First, we need to multiply the two binomials $(1-p)$ and $(\frac{1}{2}-p)$ together. $(1-p)(\frac{1}{2}-p) = 1*(\frac{1}{2}-p) - p*(\frac{1}{2}-p)$
Distribute terms: Now, distribute the terms within the parentheses. $\newline$ \(1\times\left(\frac{ $1$ }{ $2$ }-p\right) - p\times\left(\frac{ $1$ }{ $2$ }-p\right) = \frac{ $1$ }{ $2$ } - p - \left(\frac{p}{ $2$ }\right) + p^ $2$
Combine like terms: Combine like terms. $\newline$ $\frac{1}{2} - p - \frac{p}{2} + p^2 = \frac{1}{2} - \frac{3p}{2} + p^2$
Reduce expression by P: Now, we need to reduce this expression by P, which means we subtract P from the expression we obtained. $\frac{1}{2} - \frac{3p}{2} + p^2$ - P
Subtract P: Subtract $P$ from the expression. $\left(\frac{1}{2} - \frac{3p}{2} + p^2\right) - P = \frac{1}{2} - \frac{3p}{2} + p^2 - P$
Combine like terms with P: Combine $P$ with the like terms, noting that $P$ is the same as $1*P$ or $p/1$ . $\newline$ $\frac{1}{2} - \frac{3p}{2} + p^2 - \frac{p}{1} = \frac{1}{2} - \frac{5p}{2} + p^2$
Final simplified expression: The final simplified expression is: $\frac{1}{2} - \frac{5p}{2} + p^2$