Find the product. Simplify your answer: 8(-3w² + w - 1)
Understand the Problem
The question is asking to find the product of the expression 8 times the polynomial (-3w² + w - 1) and simplify the result. This involves distributing the 8 across each term in the polynomial.
Answer
The simplified product is $$-24w^2 + 8w - 8$$.
Answer for screen readers
The simplified product is: $$-24w^2 + 8w - 8$$
Steps to Solve
- Distribute the 8 to each term in the polynomial
Start by multiplying 8 with each term inside the parentheses:
$$8 \cdot (-3w^2), \quad 8 \cdot w, \quad and \quad 8 \cdot (-1)$$
- Calculate each multiplication
Now calculate each of the products:
-
For the first term:
$$8 \cdot (-3w^2) = -24w^2$$ -
For the second term:
$$8 \cdot w = 8w$$ -
For the third term:
$$8 \cdot (-1) = -8$$
- Combine the results
Combine the results of the multiplications to write the final expression:
$$-24w^2 + 8w - 8$$
The simplified product is: $$-24w^2 + 8w - 8$$
More Information
This expression represents a polynomial where each coefficient has been multiplied by 8. Distributing allows us to simplify the polynomial effectively.
Tips
- Forgetting to distribute to all terms in the polynomial. Make sure to multiply each term.
- Mixing up the signs while distributing. Double-check the signs, especially with negative coefficients.
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