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Which expression is equivalent to ?A B C D
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Q. Which expression is equivalent to ?A B C D
- Use Distributive Property: To find the equivalent expression, we need to use the distributive property to multiply the two binomials. This is also known as the FOIL method, which stands for First, Outer, Inner, Last, referring to the terms in each binomial that need to be multiplied together.
- Multiply First Terms: First, we multiply the first terms in each binomial: (\frac{\(3\)}{\(2\)})p \times (\frac{\(1\)}{\(2\)})p = (\frac{\(3\)}{\(4\)})p^\(2\.
- Multiply Outer Terms: Next, we multiply the outer terms: .
- Multiply Inner Terms: Then, we multiply the inner terms: $\(1\) \times \left(\frac{\(1\)}{\(2\)}\right)p = \left(\frac{\(1\)}{\(2\)}\right)p.
- Multiply Last Terms: Finally, we multiply the last terms in each binomial: \(1 \times 3 = 3\).
- Add All Products: Now, we add all the products together: \(\frac{3}{4}p^2 + \frac{9}{2}p + \frac{1}{2}p + 3\).
- Combine Like Terms: We combine like terms: \((\frac{9}{2})p\) and \((\frac{1}{2})p\) are like terms, so we add them together to get \((\frac{10}{2})p\), which simplifies to \(5p\).
- Final Expression: The final expression is \((\frac{3}{4})p^2 + 5p + 3\), which matches one of the answer choices.
