Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52x2 - 120x) + 144
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25x2-120x+144
The first term is, 25x2 its coefficient is 25 .
The middle term is, -120x its coefficient is -120 .
The last term, "the constant", is +144
Step-1 : Multiply the coefficient of the first term by the constant 25 • 144 = 3600
Step-2 : Find two factors of 3600 whose sum equals the coefficient of the middle term, which is -120 .
| -3600 | + | -1 | = | -3601 | ||
| -1800 | + | -2 | = | -1802 | ||
| -1200 | + | -3 | = | -1203 | ||
| -900 | + | -4 | = | -904 | ||
| -720 | + | -5 | = | -725 | ||
| -600 | + | -6 | = | -606 | ||
| -450 | + | -8 | = | -458 | ||
| -400 | + | -9 | = | -409 | ||
| -360 | + | -10 | = | -370 | ||
| -300 | + | -12 | = | -312 | ||
| -240 | + | -15 | = | -255 | ||
| -225 | + | -16 | = | -241 | ||
| -200 | + | -18 | = | -218 | ||
| -180 | + | -20 | = | -200 | ||
| -150 | + | -24 | = | -174 | ||
| -144 | + | -25 | = | -169 | ||
| -120 | + | -30 | = | -150 | ||
| -100 | + | -36 | = | -136 | ||
| -90 | + | -40 | = | -130 | ||
| -80 | + | -45 | = | -125 | ||
| -75 | + | -48 | = | -123 | ||
| -72 | + | -50 | = | -122 | ||
| -60 | + | -60 | = | -120 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -60 and -60
25x2 - 60x - 60x - 144
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (5x-12)
Add up the last 2 terms, pulling out common factors :
12 • (5x-12)
Step-5 : Add up the four terms of step 4 :
(5x-12) • (5x-12)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (5x-12) by (5x-12)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (5x-12) and the exponents are :
1 , as (5x-12) is the same number as (5x-12)1
and 1 , as (5x-12) is the same number as (5x-12)1
The product is therefore, (5x-12)(1+1) = (5x-12)2
Final result :
(5x - 12)2
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