Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52x2 - 40x) + 16
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25x2-40x+16
The first term is, 25x2 its coefficient is 25 .
The middle term is, -40x its coefficient is -40 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 25 • 16 = 400
Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is -40 .
| -400 | + | -1 | = | -401 | ||
| -200 | + | -2 | = | -202 | ||
| -100 | + | -4 | = | -104 | ||
| -80 | + | -5 | = | -85 | ||
| -50 | + | -8 | = | -58 | ||
| -40 | + | -10 | = | -50 | ||
| -25 | + | -16 | = | -41 | ||
| -20 | + | -20 | = | -40 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -20
25x2 - 20x - 20x - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x-4)
Add up the last 2 terms, pulling out common factors :
4 • (5x-4)
Step-5 : Add up the four terms of step 4 :
(5x-4) • (5x-4)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (5x-4) by (5x-4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x-4) and the exponents are :
1 , as (5x-4) is the same number as (5x-4)1
and 1 , as (5x-4) is the same number as (5x-4)1
The product is therefore, (5x-4)(1+1) = (5x-4)2
Final result :
(5x - 4)2
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