Find the product. Simplify your answer: 4(-x² + 9)
Understand the Problem
The question is asking to find the product of a mathematical expression and simplify the result. Specifically, it involves multiplying 4 by the expression (-x² + 9).
Answer
The simplified expression is $$ -4x^2 + 36 $$.
Answer for screen readers
The simplified expression is: $$ -4x^2 + 36 $$
Steps to Solve
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Distribute the 4
Multiply each term in the expression by 4.The expression is given as: $$ 4(-x^2 + 9) $$
Distributing gives:
$$ 4 \cdot (-x^2) + 4 \cdot 9 $$ -
Calculate the products
Now, calculate each multiplication:-
For the first term:
$$ 4 \cdot (-x^2) = -4x^2 $$ -
For the second term:
$$ 4 \cdot 9 = 36 $$
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Combine the results
Combine the results from the previous step:
$$ -4x^2 + 36 $$
Thus, the simplified expression is:
$$ -4x^2 + 36 $$
The simplified expression is: $$ -4x^2 + 36 $$
More Information
This result is a polynomial in standard form, where the terms are listed in descending order of the degree of $x$. The expression can also be factored further if needed, using techniques such as factoring out a common factor.
Tips
- Forgetting to distribute the 4 to both terms in the parentheses.
- Incorrectly adding or multiplying the coefficients. Always double-check each calculation to ensure accuracy.
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