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the distributive property to remove the parentheses. \( -3(4 x-3 w-5) \)

Ask by Conner Deleon. in the United States
Jan 21,2025

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Answer

Apply the distributive property by multiplying \(-3\) with each term inside the parentheses: \(-3 \times 4x = -12x\), \(-3 \times -3w = 9w\), and \(-3 \times -5 = 15\). The simplified expression is \(-12x + 9w + 15\).

Solution

Simplify the expression by following steps: - step0: Rearrange the terms: \(-3\left(4x-3w-5\right)\) - step1: Rearrange the terms: \(-12x+9w+15\) To apply the distributive property to the expression \( -3(4x - 3w - 5) \), we multiply each term inside the parentheses by \(-3\): 1. Multiply \(-3\) by \(4x\): \[ -3 \cdot 4x = -12x \] 2. Multiply \(-3\) by \(-3w\): \[ -3 \cdot -3w = 9w \] 3. Multiply \(-3\) by \(-5\): \[ -3 \cdot -5 = 15 \] Now, combine all the results: \[ -12x + 9w + 15 \] Thus, the expression without parentheses is: \[ -12x + 9w + 15 \]

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Mind Expander

When you apply the distributive property to \( -3(4x - 3w - 5) \), you multiply each term inside the parentheses by \(-3\). This results in: \[ -3 \times 4x = -12x, \quad -3 \times -3w = 9w, \quad -3 \times -5 = 15. \] Putting it all together, you get the expression: \[ -12x + 9w + 15. \] If you find yourself struggling with signs while distributing, it can help to write out the multiplication clearly step by step. A common mistake is to overlook the negative signs; always keep an eye out for them! Remember, two negatives make a positive, so \(-3 \times -3w\) equals \(9w\).

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