what is the factored form of w^{2}+12w+36
PLZ HELP
(w+6)^2
To find the factored form of the given quadratic expression w^2 + 12w + 36, we need to factorize it.
Step 1: Identify the factors of the constant term (36) that add up to the coefficient of the linear term (12).
In this case, the factors of 36 that add up to 12 are 6 and 6.
Step 2: Rewrite the quadratic expression using the factors identified in step 1.
w^2 + 6w + 6w + 36
Step 3: Group the terms in pairs.
(w^2 + 6w) + (6w + 36)
Step 4: Factor out the greatest common factor from each group.
w(w + 6) + 6(w + 6)
Step 5: Notice that the terms in parentheses are the same.
(w + 6)(w + 6)
Step 6: Simplify the expression.
(w + 6)^2
Therefore, the factored form of w^2 + 12w + 36 is (w + 6)^2.
To find the factored form of the quadratic expression \(w^{2}+12w+36\), you can use the factoring method.
Step 1: Look for two numbers that, when multiplied, give you the constant term (36), and when added, give you the coefficient of the middle term (12).
In this case, the middle term is 12, and the constant term is 36. The only pair of numbers that satisfies this condition is 6 and 6 (since 6 * 6 = 36 and 6 + 6 = 12).
Step 2: Rewrite the quadratic expression using these two numbers.
\(w^{2} + 6w + 6w + 36\)
Step 3: Group the terms.
\((w^{2} + 6w) + (6w + 36)\)
Step 4: Factor out the greatest common factor from each group.
\(w(w + 6) + 6(w + 6)\)
Step 5: Notice that the two groups have a common factor of (w + 6). Factor this out.
\((w + 6)(w + 6)\)
Step 6: Simplify the expression.
\((w + 6)^{2}\)
Therefore, the factored form of \(w^{2} + 12w + 36\) is \((w + 6)^{2}\).