Question

Factor the expression. $$x^{2}+18 x+81$$

Short answer

The factored form of the expression \(x^{2}+18 x+81\) is \((x + 9) (x + 9)\) or \((x + 9)^{2}\).

Step-by-step solution

Identify the type of quadratic

The given expression is a quadratic of the form \(ax^{2}+bx+c\). This general form is often applicable to most quadratic expressions.

Find the factors

To factorize this expression, one should look for two numbers that multiply to give \(a*c (1*81 = 81)\), and add up to give \(b (18)\). In this case, the numbers 9 and 9 satisfy these conditions because \(9*9 = 81\) and \(9+9 = 18\).

Write in Factored Form

Now, replace \(b\) in the general quadratic form with the two factors found in step 2. Express the quadratic in its factored form as \(a(x-h)(x-k)\) where \(h\) and \(k\) are the solutions from step 2. Proceed as follows: \(x^{2}+18 x+81\) can be written as \((x + 9) (x + 9)\).