Find the product of 2k - 5 and 3k + 6.
Understand the Problem
The question is asking for the product of two algebraic expressions: 2k - 5 and 3k + 6. To solve it, we will apply the distributive property (also known as the FOIL method for binomials).
Answer
The product of $2k - 5$ and $3k + 6$ is $6k^2 - 3k - 30$.
Answer for screen readers
The product of $2k - 5$ and $3k + 6$ is $6k^2 - 3k - 30$.
Steps to Solve
- Identify the expressions to multiply
We need to multiply the two algebraic expressions: $2k - 5$ and $3k + 6$.
- Apply the distributive property (FOIL method)
Using the distributive property, we will multiply each term in the first expression by each term in the second expression.
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First: $2k \cdot 3k = 6k^2$
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Outer: $2k \cdot 6 = 12k$
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Inner: $-5 \cdot 3k = -15k$
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Last: $-5 \cdot 6 = -30$
- Combine like terms
Now we combine the results from the previous step:
$$6k^2 + 12k - 15k - 30$$
Combine $12k$ and $-15k$:
$$6k^2 - 3k - 30$$
The product of $2k - 5$ and $3k + 6$ is $6k^2 - 3k - 30$.
More Information
This expression represents the expanded form of the product of two binomials. The degree of the resulting polynomial is 2 since the highest power of $k$ is $k^2$.
Tips
- Forgetting to combine like terms at the end.
- Misapplying the distributive property by not multiplying every term correctly.
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