Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+18x+81
The first term is, x2 its coefficient is 1 .
The middle term is, +18x 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
x2 + 9x + 9x + 81
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+9)
Add up the last 2 terms, pulling out common factors :
9 • (x+9)
Step-5 : Add up the four terms of step 4 :
(x+9) • (x+9)
Which is the desired factorization
Multiplying Exponential Expressions :
1.2 Multiply (x+9) by (x+9)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+9) and the exponents are :
1 , as (x+9) is the same number as (x+9)1
and 1 , as (x+9) is the same number as (x+9)1
The product is therefore, (x+9)(1+1) = (x+9)2
Final result :
(x + 9)2
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