(w-(3)/(2))(w+(7)/(2)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) ((w-3)(w+7))/(2) (B) ((2w+7)(2w-3))/(2) (c) ((w-3)(w+7))/(4) (D) ((2w+7)(2w-3))/(4)

Simplify the expression: Now, we simplify the expression by combining like terms and multiplying the constants. w^2 + (7/2)w - (3/2)w - (3*7)/(2*2) w^2 + (7w - 3w)/2 - 21/4 w^2 + (4w)/2 - 21/4 w^2 + 2w - 21/4Check answer choices: We can see that none of the answer choices match the simplified form w^2 + 2w - 21/4 exactly. However, we need to check if any of the answer choices can be simplified to this form. Let's check each answer choice to see if any of them simplify to w^2 + 2w - 21/4.Checking choice (A): Checking choice (A): ((w-3)(w+7))/2 This simplifies to (w^2 + 4w - 21)/2, which is not the same as w^2 + 2w - 21/4.Checking choice (B): Checking choice (B): ((2w+7)(2w-3))/2 This simplifies to (4w^2 - 9 + 14w)/2, which is not the same as w^2 + 2w - 21/4.Checking choice (C): Checking choice (C): ((w-3)(w+7))/4 This simplifies to (w^2 + 4w - 21)/4, which is not the same as w^2 + 2w - 21/4.Checking choice (D): Checking choice (D): ((2w+7)(2w-3))/4 This simplifies to (4w^2 + 14w - 6w - 21)/4, which simplifies further to (4w^2 + 8w - 21)/4. If we divide each term by 4, we get w^2 + 2w - 21/4, which matches our simplified expression.

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(w-(3)/(2))(w+(7)/(2))
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
((w-3)(w+7))/(2)
(B)
((2w+7)(2w-3))/(2)
(c)
((w-3)(w+7))/(4)
(D)
((2w+7)(2w-3))/(4)

$\left(w-\frac{3}{2}\right)\left(w+\frac{7}{2}\right)$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{(w-3)(w+7)}{2}$ $\newline$ (B) $\frac{(2 w+7)(2 w-3)}{2}$ $\newline$ (C) $\frac{(w-3)(w+7)}{4}$ $\newline$ (D) $\frac{(2 w+7)(2 w-3)}{4}$

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Full solution

\left(w-\frac{3}{2}\right)\left(w+\frac{7}{2}\right)

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

\frac{(w-3)(w+7)}{2}

\newline

(B)

\frac{(2 w+7)(2 w-3)}{2}

\newline

(C)

\frac{(w-3)(w+7)}{4}

\newline

(D)

\frac{(2 w+7)(2 w-3)}{4}

Simplify the expression: Now, we simplify the expression by combining like terms and multiplying the constants. $\newline$ $w^2 + \frac{7}{2}w - \frac{3}{2}w - \frac{3 \times 7}{2 \times 2}$ $\newline$ $w^2 + \frac{7w - 3w}{2} - \frac{21}{4}$ $\newline$ $w^2 + \frac{4w}{2} - \frac{21}{4}$ $\newline$ $w^2 + 2w - \frac{21}{4}$
Check answer choices: We can see that none of the answer choices match the simplified form $w^2 + 2w - \frac{21}{4}$ exactly. However, we need to check if any of the answer choices can be simplified to this form. $\newline$ Let's check each answer choice to see if any of them simplify to $w^2 + 2w - \frac{21}{4}$ .
Checking choice (A): Checking choice (A): $\newline$ $(\frac{(w-3)(w+7)}{2})$ $\newline$ This simplifies to $(\frac{w^2 + 4w - 21}{2})$ , which is not the same as $w^2 + 2w - \frac{21}{4}$ .
Checking choice (B): Checking choice (B): $\newline$ $(\frac{(2w+7)(2w-3)}{2})$ $\newline$ This simplifies to $(\frac{4w^2 - 9 + 14w}{2})$ , which is not the same as $w^2 + 2w - \frac{21}{4}$ .
Checking choice (C): Checking choice (C): $\newline$ $(\frac{(w-3)(w+7)}{4})$ $\newline$ This simplifies to $(\frac{w^2 + 4w - 21}{4})$ , which is not the same as $w^2 + 2w - \frac{21}{4}$ .
Checking choice (D): Checking choice (D): $\newline$ $(\frac{(2w+7)(2w-3)}{4})$ $\newline$ This simplifies to $(\frac{4w^2 + 14w - 6w - 21}{4})$ , which simplifies further to $(\frac{4w^2 + 8w - 21}{4})$ . $\newline$ If we divide each term by $4$ , we get $w^2 + 2w - \frac{21}{4}$ , which matches our simplified expression.