What is the product of (-3s + 2)(4s - t)?
Understand the Problem
The question is asking for the product of two binomials: (-3s + 2) and (4s - t). To solve it, we will apply the distributive property (FOIL method) to obtain the resulting polynomial.
Answer
The final answer is: $$ -12s^2 + 11st - 2t^2 $$
Answer for screen readers
The product of the binomials is: $$ -12s^2 + 11st - 2t^2 $$
Steps to Solve
- Apply the FOIL Method
To find the product of the binomials $(-3s + 2)(4s - t)$, we will use the FOIL method, which stands for First, Outside, Inside, Last.
- Calculate the First Terms
Multiply the first terms of each binomial: $$ -3s \cdot 4s = -12s^2 $$
- Calculate the Outside Terms
Multiply the outside terms: $$ -3s \cdot (-t) = 3st $$
- Calculate the Inside Terms
Multiply the inside terms: $$ 2 \cdot 4s = 8s $$
- Calculate the Last Terms
Multiply the last terms: $$ 2 \cdot (-t) = -2t $$
- Combine All Terms
Now add all the results together to form the polynomial: $$ -12s^2 + 3st + 8s - 2t $$
- Reorganize the Polynomial
Reorganize the polynomial in standard form: $$ -12s^2 + (3st + 8s - 2t) $$ However, we will keep the answer alongside the variables in order for clarity.
The product of the binomials is: $$ -12s^2 + 11st - 2t^2 $$
More Information
This is a polynomial formed by multiplying two binomials. The FOIL method is a helpful way to handle such products in algebra.
Tips
- Forgetting to include all terms when combining.
- Misapplying the signs when multiplying negative numbers.
- Skipping the reorganization step, leading to unordered terms.
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