Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-20x+100
The first term is, x2 its coefficient is 1 .
The middle term is, -20x its coefficient is -20 .
The last term, "the constant", is +100
Step-1 : Multiply the coefficient of the first term by the constant 1 • 100 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .
| -100 | + | -1 | = | -101 | ||
| -50 | + | -2 | = | -52 | ||
| -25 | + | -4 | = | -29 | ||
| -20 | + | -5 | = | -25 | ||
| -10 | + | -10 | = | -20 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10
x2 - 10x - 10x - 100
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-10)
Add up the last 2 terms, pulling out common factors :
10 • (x-10)
Step-5 : Add up the four terms of step 4 :
(x-10) • (x-10)
Which is the desired factorization
Multiplying Exponential Expressions :
1.2 Multiply (x-10) by (x-10)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-10) and the exponents are :
1 , as (x-10) is the same number as (x-10)1
and 1 , as (x-10) is the same number as (x-10)1
The product is therefore, (x-10)(1+1) = (x-10)2
Final result :
(x - 10)2
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