Answer:
(n + 9)^2
Explanation:
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+18n+81
The first term is, n2 its coefficient is 1 .
The middle term is, +18n its coefficient is 18 .
The last term, "the constant", is +81
Step-1 : Multiply the coefficient of the first term by the constant 1 • 81 = 81
Step-2 : Find two factors of 81 whose sum equals the coefficient of the middle term, which is 18 .
-81 + -1 = -82
-27 + -3 = -30
-9 + -9 = -18
-3 + -27 = -30
-1 + -81 = -82
1 + 81 = 82
3 + 27 = 30
9 + 9 = 18 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 9 and 9
n2 + 9n + 9n + 81
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n+9)
Add up the last 2 terms, pulling out common factors :
9 • (n+9)
Step-5 : Add up the four terms of step 4 :
(n+9) • (n+9)
Which is the desired factorization
Multiplying Exponential Expressions :
1.2 Multiply (n+9) by (n+9)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (n+9) and the exponents are :
1 , as (n+9) is the same number as (n+9)1
and 1 , as (n+9) is the same number as (n+9)1
The product is therefore, (n+9)(1+1) = (n+9)2
Final result :
(n + 9)^2
Processing ends successfully
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