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Simplify: −4(2x+5)

(1 point)
A. (-4 + 2x) x (-4 + 5)
B. (-4 x 2x) + (-4 x 5)
C. (-4 - 2x) + (-4 - 5)
D. (-4 / 2x) + (-4 / 5)

3 answers

To simplify the expression \(-4(2x + 5)\), we can use the distributive property:

\[ -4(2x + 5) = -4 \cdot 2x + -4 \cdot 5 \]

Calculating each term:

\[ -4 \cdot 2x = -8x \] \[ -4 \cdot 5 = -20 \]

Now, combining these results gives:

\[ -8x - 20 \]

Now let's check the answer choices given:

A. \((-4 + 2x) \times (-4 + 5)\) - This does not simplify to \(-8x - 20\).

B. \((-4 \times 2x) + (-4 \times 5)\) - This simplifies to \(-8x - 20\), which is correct.

C. \((-4 - 2x) + (-4 - 5)\) - This does not simplify to \(-8x - 20\).

D. \((-4 / 2x) + (-4 / 5)\) - This does not simplify to \(-8x - 20\).

The correct answer is:

B. \((-4 \times 2x) + (-4 \times 5)\)

Is This correct?

Yes, the simplification I provided for the expression \(-4(2x + 5)\) is correct, and option B accurately represents that calculation.

To clarify:

  • By applying the distributive property, we simplified the expression as follows:

    • \(-4(2x + 5) = -4 \cdot 2x + (-4) \cdot 5 = -8x - 20\).

  • Option B states \((-4 \times 2x) + (-4 \times 5)\), which simplifies to \(-8x - 20\).

Thus, option B is indeed the correct choice. Thank you for your patience!