QQuestionMathematics
QuestionMathematics
"What is the product of (a − 5) and (a + 3)?
A. A^2 − 15
B. A^2 + 2a − 15
C. A^2 − 2a − 15
D. A − 5 − 2"
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Answer
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Step 1:: To find the product of two binomials, we use the distributive property (also known as FOIL: First, Outer, Inner, Last) and multiply each term in the first binomial by each term in the second binomial.
The binomials given are (a - 5) and (a + 3).
Step 2:: Multiply the first term in the first binomial by the first term in the second binomial: a * a = a^2
Step 3:: Multiply the first term in the first binomial by the second term in the second binomial: a * 3 = 3a
Step 4:: Multiply the second term in the first binomial by the first term in the second binomial: - 5 * a = - 5a
Step 5:: Multiply the second term in the first binomial by the second term in the second binomial: - 5 * 3 = - 15
Step 6:: Combine the results from Steps 2 - 5: a^2 + 3a - 5a - 15
Step 7:: Combine like terms: a^2 - 2a - 15
Final Answer
The product of (a - 5) and (a + 3) is a^2 - 2a - 15, which corresponds to option B.
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