Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(24x2 - 72x) + 81
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 16x2-72x+81
The first term is, 16x2 its coefficient is 16 .
The middle term is, -72x its coefficient is -72 .
The last term, "the constant", is +81
Step-1 : Multiply the coefficient of the first term by the constant 16 • 81 = 1296
Step-2 : Find two factors of 1296 whose sum equals the coefficient of the middle term, which is -72 .
| -1296 | + | -1 | = | -1297 | ||
| -648 | + | -2 | = | -650 | ||
| -432 | + | -3 | = | -435 | ||
| -324 | + | -4 | = | -328 | ||
| -216 | + | -6 | = | -222 | ||
| -162 | + | -8 | = | -170 | ||
| -144 | + | -9 | = | -153 | ||
| -108 | + | -12 | = | -120 | ||
| -81 | + | -16 | = | -97 | ||
| -72 | + | -18 | = | -90 | ||
| -54 | + | -24 | = | -78 | ||
| -48 | + | -27 | = | -75 | ||
| -36 | + | -36 | = | -72 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -36
16x2 - 36x - 36x - 81
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (4x-9)
Add up the last 2 terms, pulling out common factors :
9 • (4x-9)
Step-5 : Add up the four terms of step 4 :
(4x-9) • (4x-9)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (4x-9) by (4x-9)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (4x-9) and the exponents are :
1 , as (4x-9) is the same number as (4x-9)1
and 1 , as (4x-9) is the same number as (4x-9)1
The product is therefore, (4x-9)(1+1) = (4x-9)2
Final result :
(4x - 9)2
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