Evaluate

n^{2}-\frac{13n}{2}+3

Expand

n^{2}-\frac{13n}{2}+3

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n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

Express -6\left(-\frac{1}{2}\right) as a single fraction.

n^{2}-\frac{13}{2}n+\frac{6}{2}

Multiply -6 and -1 to get 6.

n^{2}-\frac{13}{2}n+3

Divide 6 by 2 to get 3.

n^{2}+n\left(-\frac{1}{2}\right)-6n-6\left(-\frac{1}{2}\right)

Apply the distributive property by multiplying each term of n-6 by each term of n-\frac{1}{2}.

n^{2}-\frac{13}{2}n-6\left(-\frac{1}{2}\right)

Combine n\left(-\frac{1}{2}\right) and -6n to get -\frac{13}{2}n.

n^{2}-\frac{13}{2}n+\frac{-6\left(-1\right)}{2}

Express -6\left(-\frac{1}{2}\right) as a single fraction.

n^{2}-\frac{13}{2}n+\frac{6}{2}

Multiply -6 and -1 to get 6.

n^{2}-\frac{13}{2}n+3

Divide 6 by 2 to get 3.

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