Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•32x2) - 84x) + 49
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 36x2-84x+49
The first term is, 36x2 its coefficient is 36 .
The middle term is, -84x its coefficient is -84 .
The last term, "the constant", is +49
Step-1 : Multiply the coefficient of the first term by the constant 36 • 49 = 1764
Step-2 : Find two factors of 1764 whose sum equals the coefficient of the middle term, which is -84 .
| -1764 | + | -1 | = | -1765 | ||
| -882 | + | -2 | = | -884 | ||
| -588 | + | -3 | = | -591 | ||
| -441 | + | -4 | = | -445 | ||
| -294 | + | -6 | = | -300 | ||
| -252 | + | -7 | = | -259 | ||
| -196 | + | -9 | = | -205 | ||
| -147 | + | -12 | = | -159 | ||
| -126 | + | -14 | = | -140 | ||
| -98 | + | -18 | = | -116 | ||
| -84 | + | -21 | = | -105 | ||
| -63 | + | -28 | = | -91 | ||
| -49 | + | -36 | = | -85 | ||
| -42 | + | -42 | = | -84 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -42 and -42
36x2 - 42x - 42x - 49
Step-4 : Add up the first 2 terms, pulling out like factors :
6x • (6x-7)
Add up the last 2 terms, pulling out common factors :
7 • (6x-7)
Step-5 : Add up the four terms of step 4 :
(6x-7) • (6x-7)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (6x-7) by (6x-7)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (6x-7) and the exponents are :
1 , as (6x-7) is the same number as (6x-7)1
and 1 , as (6x-7) is the same number as (6x-7)1
The product is therefore, (6x-7)(1+1) = (6x-7)2
Final result :
(6x - 7)2
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