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(-2j^(2))*((1)/(4))+((1)/(2)j^(2)-1)
Which of the following expressions is equivalent to the given expression?
Choose 1 answer:
(A) -1
(B)
(3)/(8)j^(2)-1
(C)
((j)/(2)+1)((j)/(2)-1)
(D)
(j+1)(j-1)

$\left(-2 j^{2}\right) \cdot\left(\frac{1}{4}\right)+\left(\frac{1}{2} j^{2}-1\right)$ $\newline$ Which of the following expressions is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ $\newline$ (B) $\frac{3}{8} j^{2}-1$ $\newline$ (C) $\left(\frac{j}{2}+1\right)\left(\frac{j}{2}-1\right)$ $\newline$ (D) $(j+1)(j-1)$

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Multiplication with rational exponents

Full solution

Q.

\left(-2 j^{2}\right) \cdot\left(\frac{1}{4}\right)+\left(\frac{1}{2} j^{2}-1\right)

\newline

Which of the following expressions is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

-1

\newline

(B)

\frac{3}{8} j^{2}-1

\newline

(C)

\left(\frac{j}{2}+1\right)\left(\frac{j}{2}-1\right)

\newline

(D)

(j+1)(j-1)

Simplify Multiplication: First, let's simplify the expression $(-2j^{2})\cdot\left(\frac{1}{4}\right)+\left(\frac{1}{2}j^{2}-1\right)$ by handling the multiplication and addition separately.
Handle Multiplication: We start with the multiplication part: $(-2j^{2})*\left(\frac{1}{4}\right)$ . Since $j^2$ is equal to $-1$ (because $j$ is the imaginary unit), we can replace $j^2$ with $-1$ . $\newline$ $(-2 \times -1) \times \left(\frac{1}{4}\right) = \frac{2}{4} = \frac{1}{2}$ .
Simplify Addition: Now let's simplify the addition part: $\left(\frac{1}{2}j^{2}-1\right)$ . Again, replacing $j^2$ with $-1$ , we get: $\left(\frac{1}{2} \times -1\right) - 1 = -\frac{1}{2} - 1 = -\frac{1}{2} - \frac{2}{2} = -\frac{3}{2}$ .
Combine Simplified Parts: Combine the two parts we've simplified: $\frac{1}{2} + \left(-\frac{3}{2}\right)$ . $\frac{1}{2} - \frac{3}{2} = -\frac{2}{2} = -1$ .
Final Result: The simplified expression is $-1$ , which matches option $(A)$ .

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