Factor.
$c^{2} + 6 c + 9$

Answer

Expert–verified

Hide Steps

Answer

So, the final answer is $c^{2} + 6 c + 9 = (c + 3)^{2}$ .

Steps

Step 1 ： $c^{2}$ and $9$ are perfect squares, since $c^{2} = (c)^{2}$ and $9 = (3)^{2}$ .

Step 2 ： $6 c$ is twice the product of the roots of $c^{2}$ and $9$ , since $6 c = 2 (c) (3)$ .

Step 3 ：So, $c^{2} + 6 c + 9 = (c)^{2} + 2 (c) (3) + (3)^{2}$ .

Step 4 ：We can use the square of a sum pattern to factor: $a^{2} + 2 a b + b^{2} = (a + b)^{2}$ . In this case, $a = c$ and $b = 3$ .

Step 5 ：Therefore, $(c)^{2} + 2 (c) (3) + (3)^{2} = (c + 3)^{2}$ .

Step 6 ：In conclusion, $c^{2} + 6 c + 9 = (c + 3)^{2}$ .

Step 7 ：You can always check your factorization by expanding it.

Step 8 ：So, the final answer is $c^{2} + 6 c + 9 = (c + 3)^{2}$ .