Questions: Simplify the polynomial (4n^2+3n-5)-(2n^2+3n+6)

Transcript text: Simplify the polynomial $\left(4 n^{2}+3 n-5\right)-\left(2 n^{2}+3 n+\right.$ 6)

Solution

Solution Steps

Step 1: Distribute the negative sign

Distribute the negative sign to each term inside the second set of parentheses: \[ (4n^{2} + 3n - 5) - (2n^{2} + 3n + 6) = 4n^{2} + 3n - 5 - 2n^{2} - 3n - 6 \]

Step 2: Combine like terms

Combine the terms with the same degree of $ n $:

$ 4n^{2} - 2n^{2} = 2n^{2} $
$ 3n - 3n = 0 $
$ -5 - 6 = -11 $

Step 3: Write the simplified polynomial

Combine the results from Step 2 to write the simplified polynomial: \[ 2n^{2} - 11 \]

Final Answer

$\boxed{2n^{2} - 11}$

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