Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 12x) + 9
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+12x+9
The first term is, 4x2 its coefficient is 4 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 12 .
| -36 | + | -1 | = | -37 | ||
| -18 | + | -2 | = | -20 | ||
| -12 | + | -3 | = | -15 | ||
| -9 | + | -4 | = | -13 | ||
| -6 | + | -6 | = | -12 | ||
| -4 | + | -9 | = | -13 | ||
| -3 | + | -12 | = | -15 | ||
| -2 | + | -18 | = | -20 | ||
| -1 | + | -36 | = | -37 | ||
| 1 | + | 36 | = | 37 | ||
| 2 | + | 18 | = | 20 | ||
| 3 | + | 12 | = | 15 | ||
| 4 | + | 9 | = | 13 | ||
| 6 | + | 6 | = | 12 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 6
4x2 + 6x + 6x + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+3)
Add up the last 2 terms, pulling out common factors :
3 • (2x+3)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (2x+3)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (2x+3) by (2x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x+3) and the exponents are :
1 , as (2x+3) is the same number as (2x+3)1
and 1 , as (2x+3) is the same number as (2x+3)1
The product is therefore, (2x+3)(1+1) = (2x+3)2
Final result :
(2x + 3)2
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