Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(112d2 + 220d) + 100
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 121d2+220d+100
The first term is, 121d2 its coefficient is 121 .
The middle term is, +220d its coefficient is 220 .
The last term, "the constant", is +100
Step-1 : Multiply the coefficient of the first term by the constant 121 • 100 = 12100
Step-2 : Find two factors of 12100 whose sum equals the coefficient of the middle term, which is 220 .
| -12100 | + | -1 | = | -12101 | ||
| -6050 | + | -2 | = | -6052 | ||
| -3025 | + | -4 | = | -3029 | ||
| -2420 | + | -5 | = | -2425 | ||
| -1210 | + | -10 | = | -1220 | ||
| -1100 | + | -11 | = | -1111 | ||
| -605 | + | -20 | = | -625 | ||
| -550 | + | -22 | = | -572 | ||
| -484 | + | -25 | = | -509 | ||
| -275 | + | -44 | = | -319 | ||
| -242 | + | -50 | = | -292 | ||
| -220 | + | -55 | = | -275 | ||
| -121 | + | -100 | = | -221 | ||
| -110 | + | -110 | = | -220 | ||
| -100 | + | -121 | = | -221 | ||
| -55 | + | -220 | = | -275 | ||
| -50 | + | -242 | = | -292 | ||
| -44 | + | -275 | = | -319 | ||
| -25 | + | -484 | = | -509 | ||
| -22 | + | -550 | = | -572 | ||
| -20 | + | -605 | = | -625 | ||
| -11 | + | -1100 | = | -1111 | ||
| -10 | + | -1210 | = | -1220 | ||
| -5 | + | -2420 | = | -2425 | ||
| -4 | + | -3025 | = | -3029 | ||
| -2 | + | -6050 | = | -6052 | ||
| -1 | + | -12100 | = | -12101 | ||
| 1 | + | 12100 | = | 12101 | ||
| 2 | + | 6050 | = | 6052 | ||
| 4 | + | 3025 | = | 3029 | ||
| 5 | + | 2420 | = | 2425 | ||
| 10 | + | 1210 | = | 1220 | ||
| 11 | + | 1100 | = | 1111 | ||
| 20 | + | 605 | = | 625 | ||
| 22 | + | 550 | = | 572 | ||
| 25 | + | 484 | = | 509 | ||
| 44 | + | 275 | = | 319 | ||
| 50 | + | 242 | = | 292 | ||
| 55 | + | 220 | = | 275 | ||
| 100 | + | 121 | = | 221 | ||
| 110 | + | 110 | = | 220 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 110 and 110
121d2 + 110d + 110d + 100
Step-4 : Add up the first 2 terms, pulling out like factors :
11d • (11d+10)
Add up the last 2 terms, pulling out common factors :
10 • (11d+10)
Step-5 : Add up the four terms of step 4 :
(11d+10) • (11d+10)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (11d+10) by (11d+10)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (11d+10) and the exponents are :
1 , as (11d+10) is the same number as (11d+10)1
and 1 , as (11d+10) is the same number as (11d+10)1
The product is therefore, (11d+10)(1+1) = (11d+10)2
Final result :
(11d + 10)2
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