What is the product of (1-p) and ((1)/(2)-p), all reduced by p ? Choose 1 answer: (A) (1)/(2)(1-5p+2p^(2)) (B) (1)/(2)(2-5p+2p^(2)) (c) (1)/(2)(1-3p+2p^(2)) (D) (1)/(2)(2-3p+2p^(2))

Multiply Binomials: First, we need to multiply (1-p) by ((1)/(2)-p). This is a simple multiplication of two binomials. (1-p) * ((1)/(2)-p) = (1)(1/2) - (1)p - (p)(1/2) + (p)(p)Simplify Expression: Now, we simplify the expression by combining like terms and performing the multiplication. (1-p) * ((1)/(2)-p) = 1/2 - p - p/2 + p^2Combine Like Terms: Next, we combine the terms with p. 1/2 - p - p/2 + p^2 = 1/2 - (1+1/2)p + p^2Reduce Expression by p: Simplify the coefficients of p. 1/2 - (1+1/2)p + p^2 = 1/2 - (3/2)p + p^2Combine p Terms: Now, we need to reduce this expression by p, which means we subtract p from the entire expression. (1/2 - (3/2)p + p^2) - p = 1/2 - (3/2)p + p^2 - pFactor Out 1/2: Combine the p terms. 1/2 - (3/2)p + p^2 - p = 1/2 - (5/2)p + p^2Compare with Answer Choices: Finally, we need to express the answer in the form of one of the given choices. We can factor out a 1/2 to match the answer choices. 1/2 - (5/2)p + p^2 = (1/2)(1 - 5p + 2p^2)Now, we compare our result with the given answer choices. Our result is (1/2)(1 - 5p + 2p^2), which matches answer choice (A).

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What is the product of
(1-p) and
((1)/(2)-p), all reduced by
p ?
Choose 1 answer:
(A)
(1)/(2)(1-5p+2p^(2))
(B)
(1)/(2)(2-5p+2p^(2))
(c)
(1)/(2)(1-3p+2p^(2))
(D)
(1)/(2)(2-3p+2p^(2))

What is the product of $(1-p)$ and $\left(\frac{1}{2}-p\right)$ , all reduced by $p$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2}\left(1-5 p+2 p^{2}\right)$ $\newline$ (B) $\frac{1}{2}\left(2-5 p+2 p^{2}\right)$ $\newline$ (C) $\frac{1}{2}\left(1-3 p+2 p^{2}\right)$ $\newline$ (D) $\frac{1}{2}\left(2-3 p+2 p^{2}\right)$

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Q. What is the product of

(1-p)

and

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

, all reduced by

p

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2}\left(1-5 p+2 p^{2}\right)

\newline

(B)

\frac{1}{2}\left(2-5 p+2 p^{2}\right)

\newline

(C)

\frac{1}{2}\left(1-3 p+2 p^{2}\right)

\newline

(D)

\frac{1}{2}\left(2-3 p+2 p^{2}\right)

Multiply Binomials: First, we need to multiply $(1-p)$ by $\left(\frac{1}{2}-p\right)$ . This is a simple multiplication of two binomials. $\newline$ $(1-p) \times \left(\frac{1}{2}-p\right) = (1)\left(\frac{1}{2}\right) - (1)p - (p)\left(\frac{1}{2}\right) + (p)(p)$
Simplify Expression: Now, we simplify the expression by combining like terms and performing the multiplication. $\newline$ (\(1-p) \times \left(\frac{ $1$ }{ $2$ }-p\right) = \frac{ $1$ }{ $2$ } - p - \frac{p}{ $2$ } + p^ $2$
Combine Like Terms: Next, we combine the terms with $p$ . $\frac{1}{2} - p - \frac{p}{2} + p^2 = \frac{1}{2} - (1+\frac{1}{2})p + p^2$
Reduce Expression by $p$ : Simplify the coefficients of $p$ . $\frac{1}{2} - \left(1+\frac{1}{2}\right)p + p^2 = \frac{1}{2} - \frac{3}{2}p + p^2$
Combine p Terms: Now, we need to reduce this expression by $p$ , which means we subtract $p$ from the entire expression. $\left(\frac{1}{2} - \frac{3}{2}p + p^2\right) - p = \frac{1}{2} - \frac{3}{2}p + p^2 - p$
Factor Out $1$ / $2$ : Combine the $p$ terms. $\newline$ $\frac{1}{2} - \frac{3}{2}p + p^2 - p = \frac{1}{2} - \frac{5}{2}p + p^2$
Compare with Answer Choices: Finally, we need to express the answer in the form of one of the given choices. We can factor out a $\frac{1}{2}$ to match the answer choices. $\newline$ $\frac{1}{2} - \frac{5}{2}p + p^2 = \left(\frac{1}{2}\right)(1 - 5p + 2p^2)$
Compare with Answer Choices: Finally, we need to express the answer in the form of one of the given choices. We can factor out a $\frac{1}{2}$ to match the answer choices. $\newline$ $\frac{1}{2} - \frac{5}{2}p + p^2 = \left(\frac{1}{2}\right)(1 - 5p + 2p^2)$ Now, we compare our result with the given answer choices. $\newline$ Our result is $\left(\frac{1}{2}\right)(1 - 5p + 2p^2)$ , which matches answer choice (A).