Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2−6n

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asked Mar 12, 2024 88.9k views

1 Answer

Matheus Hatje · Answer 1 · 2024-03-17T05:08:46+0000

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Given expression:
$\displaystyle\sf n^(2) -6n$

1. Take half of the coefficient of the linear term:

Half of
$\displaystyle\sf -6n$ is
$\displaystyle\sf -(6)/(2) = -3$ .

2. Square the result obtained in step 1:

Squaring
$\displaystyle\sf -3$ gives
$\displaystyle\sf (-3)^(2) = 9$ .

3. Add the value obtained in step 2 to the original expression:

$\displaystyle\sf n^(2) -6n +9$

The result can be written as a binomial squared:

$\displaystyle\sf ( n-3)^(2)$

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