Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52x2 + 110x) + 121
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25x2+110x+121
The first term is, 25x2 its coefficient is 25 .
The middle term is, +110x its coefficient is 110 .
The last term, "the constant", is +121
Step-1 : Multiply the coefficient of the first term by the constant 25 • 121 = 3025
Step-2 : Find two factors of 3025 whose sum equals the coefficient of the middle term, which is 110 .
| -3025 | + | -1 | = | -3026 | ||
| -605 | + | -5 | = | -610 | ||
| -275 | + | -11 | = | -286 | ||
| -121 | + | -25 | = | -146 | ||
| -55 | + | -55 | = | -110 | ||
| -25 | + | -121 | = | -146 | ||
| -11 | + | -275 | = | -286 | ||
| -5 | + | -605 | = | -610 | ||
| -1 | + | -3025 | = | -3026 | ||
| 1 | + | 3025 | = | 3026 | ||
| 5 | + | 605 | = | 610 | ||
| 11 | + | 275 | = | 286 | ||
| 25 | + | 121 | = | 146 | ||
| 55 | + | 55 | = | 110 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 55 and 55
25x2 + 55x + 55x + 121
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x+11)
Add up the last 2 terms, pulling out common factors :
11 • (5x+11)
Step-5 : Add up the four terms of step 4 :
(5x+11) • (5x+11)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (5x+11) by (5x+11)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x+11) and the exponents are :
1 , as (5x+11) is the same number as (5x+11)1
and 1 , as (5x+11) is the same number as (5x+11)1
The product is therefore, (5x+11)(1+1) = (5x+11)2
Final result :
(5x + 11)2
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