Question
7 Read what Mia says. When I expand and simplify \( x(x-3)+x(x+5) \), I get the same answer as when I expand \( 2 x(x+1) \). Is Mia correct? Explain your answer.
Ask by Clark Lyons. in Egypt
Mar 08,2025
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Tutor-Verified Answer
Answer
Mia is correct because both expressions simplify to \( 2x^2 + 2x \).
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Let’s help Mia out! When we expand and simplify \( x(x-3)+x(x+5) \), we first distribute: 1. \( x(x-3) = x^2 - 3x \) 2. \( x(x+5) = x^2 + 5x \) Now, combining them gives us: \[ x^2 - 3x + x^2 + 5x = 2x^2 + 2x \] Now let’s expand \( 2x(x+1) \): 1. \( 2x(x+1) = 2x^2 + 2x \) The results are the same! So, Mia is correct; both expressions yield \( 2x^2 + 2x \). Great job, Mia!