Question
Subtract the polynomials. \( \left(-3 r^{2}+3 r+7\right)-\left(7 r^{2}+5 r-2\right) \) \( \left(-3 r^{2}+3 r+7\right)-\left(7 r^{2}+5 r-2\right)=\square \) (Simplify your answer.)
Ask by Sandoval Wheeler. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(-10r² - 2r + 9\)
Solution
To subtract the polynomials, distribute the negative sign through the second polynomial:
(-3r² + 3r + 7) - (7r² + 5r - 2)
= -3r² + 3r + 7 - 7r² - 5r + 2
Now combine like terms:
r² terms: -3r² - 7r² = -10r²
r terms: 3r - 5r = -2r
Constants: 7 + 2 = 9
So, the simplified expression is:
-10r² - 2r + 9
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Simplify this solution Extra Insights
To subtract the polynomials, you need to distribute the negative sign across the second polynomial and then combine like terms: \[ (-3 r^{2} + 3 r + 7) - (7 r^{2} + 5 r - 2) = -3 r^{2} + 3 r + 7 - 7 r^{2} - 5 r + 2 \] Now, combine the like terms: \[ (-3 r^{2} - 7 r^{2}) + (3 r - 5 r) + (7 + 2) = -10 r^{2} - 2r + 9 \] So, the simplified answer is: \[ -10 r^{2} - 2r + 9 \] Now, let's fill in the square: \[ \left(-3 r^{2}+3 r+7\right)-\left(7 r^{2}+5 r-2\right)= -10 r^{2}-2r+9 \]
