Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((2•52x2) - 60x) + 18
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
50x2 - 60x + 18 = 2 • (25x2 - 30x + 9)
Trying to factor by splitting the middle term
3.2 Factoring 25x2 - 30x + 9
The first term is, 25x2 its coefficient is 25 .
The middle term is, -30x its coefficient is -30 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 25 • 9 = 225
Step-2 : Find two factors of 225 whose sum equals the coefficient of the middle term, which is -30 .
| -225 | + | -1 | = | -226 | ||
| -75 | + | -3 | = | -78 | ||
| -45 | + | -5 | = | -50 | ||
| -25 | + | -9 | = | -34 | ||
| -15 | + | -15 | = | -30 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -15
25x2 - 15x - 15x - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x-3)
Add up the last 2 terms, pulling out common factors :
3 • (5x-3)
Step-5 : Add up the four terms of step 4 :
(5x-3) • (5x-3)
Which is the desired factorization
Multiplying Exponential Expressions :
3.3 Multiply (5x-3) by (5x-3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x-3) and the exponents are :
1 , as (5x-3) is the same number as (5x-3)1
and 1 , as (5x-3) is the same number as (5x-3)1
The product is therefore, (5x-3)(1+1) = (5x-3)2
Final result :
2 • (5x - 3)2
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