Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52x2 - 60x) + 36
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25x2-60x+36
The first term is, 25x2 its coefficient is 25 .
The middle term is, -60x its coefficient is -60 .
The last term, "the constant", is +36
Step-1 : Multiply the coefficient of the first term by the constant 25 • 36 = 900
Step-2 : Find two factors of 900 whose sum equals the coefficient of the middle term, which is -60 .
| -900 | + | -1 | = | -901 | ||
| -450 | + | -2 | = | -452 | ||
| -300 | + | -3 | = | -303 | ||
| -225 | + | -4 | = | -229 | ||
| -180 | + | -5 | = | -185 | ||
| -150 | + | -6 | = | -156 | ||
| -100 | + | -9 | = | -109 | ||
| -90 | + | -10 | = | -100 | ||
| -75 | + | -12 | = | -87 | ||
| -60 | + | -15 | = | -75 | ||
| -50 | + | -18 | = | -68 | ||
| -45 | + | -20 | = | -65 | ||
| -36 | + | -25 | = | -61 | ||
| -30 | + | -30 | = | -60 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -30 and -30
25x2 - 30x - 30x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x-6)
Add up the last 2 terms, pulling out common factors :
6 • (5x-6)
Step-5 : Add up the four terms of step 4 :
(5x-6) • (5x-6)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (5x-6) by (5x-6)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x-6) and the exponents are :
1 , as (5x-6) is the same number as (5x-6)1
and 1 , as (5x-6) is the same number as (5x-6)1
The product is therefore, (5x-6)(1+1) = (5x-6)2
Final result :
(5x - 6)2
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