Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(22x2 + 20x) + 25
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2+20x+25
The first term is, 4x2 its coefficient is 4 .
The middle term is, +20x its coefficient is 20 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 4 • 25 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is 20 .
| -100 | + | -1 | = | -101 | ||
| -50 | + | -2 | = | -52 | ||
| -25 | + | -4 | = | -29 | ||
| -20 | + | -5 | = | -25 | ||
| -10 | + | -10 | = | -20 | ||
| -5 | + | -20 | = | -25 | ||
| -4 | + | -25 | = | -29 | ||
| -2 | + | -50 | = | -52 | ||
| -1 | + | -100 | = | -101 | ||
| 1 | + | 100 | = | 101 | ||
| 2 | + | 50 | = | 52 | ||
| 4 | + | 25 | = | 29 | ||
| 5 | + | 20 | = | 25 | ||
| 10 | + | 10 | = | 20 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 10 and 10
4x2 + 10x + 10x + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (2x+5)
Add up the last 2 terms, pulling out common factors :
5 • (2x+5)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (2x+5)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (2x+5) by (2x+5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x+5) and the exponents are :
1 , as (2x+5) is the same number as (2x+5)1
and 1 , as (2x+5) is the same number as (2x+5)1
The product is therefore, (2x+5)(1+1) = (2x+5)2
Final result :
(2x + 5)2
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