Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 44x) + 121
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+44x+121
The first term is, 4x2 its coefficient is 4 .
The middle term is, +44x its coefficient is 44 .
The last term, "the constant", is +121
Step-1 : Multiply the coefficient of the first term by the constant 4 • 121 = 484
Step-2 : Find two factors of 484 whose sum equals the coefficient of the middle term, which is 44 .
| -484 | + | -1 | = | -485 | ||
| -242 | + | -2 | = | -244 | ||
| -121 | + | -4 | = | -125 | ||
| -44 | + | -11 | = | -55 | ||
| -22 | + | -22 | = | -44 | ||
| -11 | + | -44 | = | -55 | ||
| -4 | + | -121 | = | -125 | ||
| -2 | + | -242 | = | -244 | ||
| -1 | + | -484 | = | -485 | ||
| 1 | + | 484 | = | 485 | ||
| 2 | + | 242 | = | 244 | ||
| 4 | + | 121 | = | 125 | ||
| 11 | + | 44 | = | 55 | ||
| 22 | + | 22 | = | 44 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 22 and 22
4x2 + 22x + 22x + 121
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+11)
Add up the last 2 terms, pulling out common factors :
11 • (2x+11)
Step-5 : Add up the four terms of step 4 :
(2x+11) • (2x+11)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (2x+11) by (2x+11)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x+11) and the exponents are :
1 , as (2x+11) is the same number as (2x+11)1
and 1 , as (2x+11) is the same number as (2x+11)1
The product is therefore, (2x+11)(1+1) = (2x+11)2
Final result :
(2x + 11)2
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