Find the product. Simplify your answer. -5(-4r² + 2r + 1)
Understand the Problem
The question is asking to find the product of the expression -5 times the polynomial (-4r² + 2r + 1) and to simplify the result. This involves distributing -5 to each term in the polynomial.
Answer
The product is \( 20r² - 10r - 5 \).
Answer for screen readers
The simplified product is ( 20r² - 10r - 5 ).
Steps to Solve
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Distributing the first term Multiply -5 by -4r²: [ -5 \times -4r² = 20r² ]
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Distributing the second term Multiply -5 by 2r: [ -5 \times 2r = -10r ]
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Distributing the last term Multiply -5 by 1: [ -5 \times 1 = -5 ]
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Combine results Now combine all the results from the distributions: [ 20r² - 10r - 5 ]
The simplified product is ( 20r² - 10r - 5 ).
More Information
Distributing a scalar across a polynomial is a fundamental concept in algebra. This process helps you understand how coefficients affect each term in an expression.
Tips
- Forgetting to change the signs appropriately when multiplying negative numbers.
- Failing to combine all terms at the end.
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