Problem

$\left(3 x^{2}+2 x\right)-\left(8 x^{2}+7\right)$

Answer

Expert–verified
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Answer

Final Answer: \(\boxed{-5x^{2} + 2x - 7}\)

Steps

Step 1 :Given the polynomials \(3 x^{2}+2 x\) and \(8 x^{2}+7\)

Step 2 :We are asked to subtract the second polynomial from the first

Step 3 :To do this, we subtract the like terms separately

Step 4 :Subtracting the coefficients of \(x^{2}\) terms gives us \(-5x^{2}\)

Step 5 :Subtracting the constant terms gives us \(-7\)

Step 6 :The term \(2x\) remains unchanged as there is no corresponding term in the second polynomial

Step 7 :So, the result of the subtraction is \(-5x^{2} + 2x - 7\)

Step 8 :Final Answer: \(\boxed{-5x^{2} + 2x - 7}\)

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