Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(34x2 + 36x) + 4
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 81x2+36x+4
The first term is, 81x2 its coefficient is 81 .
The middle term is, +36x its coefficient is 36 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 81 • 4 = 324
Step-2 : Find two factors of 324 whose sum equals the coefficient of the middle term, which is 36 .
| -324 | + | -1 | = | -325 | ||
| -162 | + | -2 | = | -164 | ||
| -108 | + | -3 | = | -111 | ||
| -81 | + | -4 | = | -85 | ||
| -54 | + | -6 | = | -60 | ||
| -36 | + | -9 | = | -45 | ||
| -27 | + | -12 | = | -39 | ||
| -18 | + | -18 | = | -36 | ||
| -12 | + | -27 | = | -39 | ||
| -9 | + | -36 | = | -45 | ||
| -6 | + | -54 | = | -60 | ||
| -4 | + | -81 | = | -85 | ||
| -3 | + | -108 | = | -111 | ||
| -2 | + | -162 | = | -164 | ||
| -1 | + | -324 | = | -325 | ||
| 1 | + | 324 | = | 325 | ||
| 2 | + | 162 | = | 164 | ||
| 3 | + | 108 | = | 111 | ||
| 4 | + | 81 | = | 85 | ||
| 6 | + | 54 | = | 60 | ||
| 9 | + | 36 | = | 45 | ||
| 12 | + | 27 | = | 39 | ||
| 18 | + | 18 | = | 36 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 18 and 18
81x2 + 18x + 18x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
9x • (9x+2)
Add up the last 2 terms, pulling out common factors :
2 • (9x+2)
Step-5 : Add up the four terms of step 4 :
(9x+2) • (9x+2)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (9x+2) by (9x+2)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (9x+2) and the exponents are :
1 , as (9x+2) is the same number as (9x+2)1
and 1 , as (9x+2) is the same number as (9x+2)1
The product is therefore, (9x+2)(1+1) = (9x+2)2
Final result :
(9x + 2)2
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