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The expression 5x−3x(2x−5) is equivalent to which of the following?
- a)−6x2−10x
- b)−2x(3x−10)
- c)2x(2x−5)
- d)−2x(2x−5)
- e)2x(3x+5)
Correct answer is option 'B'. Can you explain this answer?
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The expression 5x−3x(2x−5) is equivalent to which of the f...
Understanding the Expression
To solve the expression \(5x - 3x(2x - 5)\), we need to simplify it step by step.
Step 1: Distributing the Terms
- Start by distributing \(-3x\) through the parentheses:
\[
-3x(2x - 5) = -3x \cdot 2x + (-3x) \cdot (-5) = -6x^2 + 15x
\]
Step 2: Combine Like Terms
- Now, substitute this back into the original expression:
\[
5x - 6x^2 + 15x
\]
- Combine the like terms \(5x\) and \(15x\):
\[
(5x + 15x) - 6x^2 = 20x - 6x^2
\]
- Rearranging gives:
\[
-6x^2 + 20x
\]
Step 3: Factoring the Result
- We can factor out \(-2x\) from the expression:
\[
-2x(3x - 10)
\]
Conclusion
- The simplified expression is \(-2x(3x - 10)\), which corresponds to option B.
In summary, through distribution, combining like terms, and factoring, we arrive at the equivalent expression of the original. Therefore, the correct answer is option B: \(-2x(3x - 10)\).
To solve the expression \(5x - 3x(2x - 5)\), we need to simplify it step by step.
Step 1: Distributing the Terms
- Start by distributing \(-3x\) through the parentheses:
\[
-3x(2x - 5) = -3x \cdot 2x + (-3x) \cdot (-5) = -6x^2 + 15x
\]
Step 2: Combine Like Terms
- Now, substitute this back into the original expression:
\[
5x - 6x^2 + 15x
\]
- Combine the like terms \(5x\) and \(15x\):
\[
(5x + 15x) - 6x^2 = 20x - 6x^2
\]
- Rearranging gives:
\[
-6x^2 + 20x
\]
Step 3: Factoring the Result
- We can factor out \(-2x\) from the expression:
\[
-2x(3x - 10)
\]
Conclusion
- The simplified expression is \(-2x(3x - 10)\), which corresponds to option B.
In summary, through distribution, combining like terms, and factoring, we arrive at the equivalent expression of the original. Therefore, the correct answer is option B: \(-2x(3x - 10)\).
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The expression 5x−3x(2x−5) is equivalent to which of the following?a)−6x2−10xb)−2x(3x−10)c)2x(2x−5)d)−2x(2x−5)e)2x(3x+5)Correct answer is option 'B'. Can you explain this answer?
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