Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(32x2 + 30x) + 25
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 9x2+30x+25
The first term is, 9x2 its coefficient is 9 .
The middle term is, +30x its coefficient is 30 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 9 • 25 = 225
Step-2 : Find two factors of 225 whose sum equals the coefficient of the middle term, which is 30 .
| -225 | + | -1 | = | -226 | ||
| -75 | + | -3 | = | -78 | ||
| -45 | + | -5 | = | -50 | ||
| -25 | + | -9 | = | -34 | ||
| -15 | + | -15 | = | -30 | ||
| -9 | + | -25 | = | -34 | ||
| -5 | + | -45 | = | -50 | ||
| -3 | + | -75 | = | -78 | ||
| -1 | + | -225 | = | -226 | ||
| 1 | + | 225 | = | 226 | ||
| 3 | + | 75 | = | 78 | ||
| 5 | + | 45 | = | 50 | ||
| 9 | + | 25 | = | 34 | ||
| 15 | + | 15 | = | 30 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 15 and 15
9x2 + 15x + 15x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x+5)
Add up the last 2 terms, pulling out common factors :
5 • (3x+5)
Step-5 : Add up the four terms of step 4 :
(3x+5) • (3x+5)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (3x+5) by (3x+5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (3x+5) and the exponents are :
1 , as (3x+5) is the same number as (3x+5)1
and 1 , as (3x+5) is the same number as (3x+5)1
The product is therefore, (3x+5)(1+1) = (3x+5)2
Final result :
(3x + 5)2
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