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 | ||
| -36 | + | -49 | = | -85 | ||
| -28 | + | -63 | = | -91 | ||
| -21 | + | -84 | = | -105 | ||
| -18 | + | -98 | = | -116 | ||
| -14 | + | -126 | = | -140 | ||
| -12 | + | -147 | = | -159 | ||
| -9 | + | -196 | = | -205 | ||
| -7 | + | -252 | = | -259 | ||
| -6 | + | -294 | = | -300 | ||
| -4 | + | -441 | = | -445 | ||
| -3 | + | -588 | = | -591 | ||
| -2 | + | -882 | = | -884 | ||
| -1 | + | -1764 | = | -1765 | ||
| 1 | + | 1764 | = | 1765 | ||
| 2 | + | 882 | = | 884 | ||
| 3 | + | 588 | = | 591 | ||
| 4 | + | 441 | = | 445 | ||
| 6 | + | 294 | = | 300 | ||
| 7 | + | 252 | = | 259 | ||
| 9 | + | 196 | = | 205 | ||
| 12 | + | 147 | = | 159 | ||
| 14 | + | 126 | = | 140 | ||
| 18 | + | 98 | = | 116 | ||
| 21 | + | 84 | = | 105 | ||
| 28 | + | 63 | = | 91 | ||
| 36 | + | 49 | = | 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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