Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 28x) + 49
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+28x+49
The first term is, 4x2 its coefficient is 4 .
The middle term is, +28x its coefficient is 28 .
The last term, "the constant", is +49
Step-1 : Multiply the coefficient of the first term by the constant 4 • 49 = 196
Step-2 : Find two factors of 196 whose sum equals the coefficient of the middle term, which is 28 .
| -196 | + | -1 | = | -197 | ||
| -98 | + | -2 | = | -100 | ||
| -49 | + | -4 | = | -53 | ||
| -28 | + | -7 | = | -35 | ||
| -14 | + | -14 | = | -28 | ||
| -7 | + | -28 | = | -35 | ||
| -4 | + | -49 | = | -53 | ||
| -2 | + | -98 | = | -100 | ||
| -1 | + | -196 | = | -197 | ||
| 1 | + | 196 | = | 197 | ||
| 2 | + | 98 | = | 100 | ||
| 4 | + | 49 | = | 53 | ||
| 7 | + | 28 | = | 35 | ||
| 14 | + | 14 | = | 28 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 14 and 14
4x2 + 14x + 14x + 49
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+7)
Add up the last 2 terms, pulling out common factors :
7 • (2x+7)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (2x+7)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (2x+7) by (2x+7)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x+7) and the exponents are :
1 , as (2x+7) is the same number as (2x+7)1
and 1 , as (2x+7) is the same number as (2x+7)1
The product is therefore, (2x+7)(1+1) = (2x+7)2
Final result :
(2x + 7)2
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