Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52x2 - 90x) + 81
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25x2-90x+81
The first term is, 25x2 its coefficient is 25 .
The middle term is, -90x its coefficient is -90 .
The last term, "the constant", is +81
Step-1 : Multiply the coefficient of the first term by the constant 25 • 81 = 2025
Step-2 : Find two factors of 2025 whose sum equals the coefficient of the middle term, which is -90 .
| -2025 | + | -1 | = | -2026 | ||
| -675 | + | -3 | = | -678 | ||
| -405 | + | -5 | = | -410 | ||
| -225 | + | -9 | = | -234 | ||
| -135 | + | -15 | = | -150 | ||
| -81 | + | -25 | = | -106 | ||
| -75 | + | -27 | = | -102 | ||
| -45 | + | -45 | = | -90 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -45 and -45
25x2 - 45x - 45x - 81
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x-9)
Add up the last 2 terms, pulling out common factors :
9 • (5x-9)
Step-5 : Add up the four terms of step 4 :
(5x-9) • (5x-9)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (5x-9) by (5x-9)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x-9) and the exponents are :
1 , as (5x-9) is the same number as (5x-9)1
and 1 , as (5x-9) is the same number as (5x-9)1
The product is therefore, (5x-9)(1+1) = (5x-9)2
Final result :
(5x - 9)2
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