Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring p2+30p+225
The first term is, p2 its coefficient is 1 .
The middle term is, +30p its coefficient is 30 .
The last term, "the constant", is +225
Step-1 : Multiply the coefficient of the first term by the constant 1 • 225 = 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
p2 + 15p + 15p + 225
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p+15)
Add up the last 2 terms, pulling out common factors :
15 • (p+15)
Step-5 : Add up the four terms of step 4 :
(p+15) • (p+15)
Which is the desired factorization
Multiplying Exponential Expressions :
1.2 Multiply (p+15) by (p+15)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (p+15) and the exponents are :
1 , as (p+15) is the same number as (p+15)1
and 1 , as (p+15) is the same number as (p+15)1
The product is therefore, (p+15)(1+1) = (p+15)2
Final result :
(p + 15)2
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