Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(72y2 + 42y) + 9
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 49y2+42y+9
The first term is, 49y2 its coefficient is 49 .
The middle term is, +42y its coefficient is 42 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 49 • 9 = 441
Step-2 : Find two factors of 441 whose sum equals the coefficient of the middle term, which is 42 .
| -441 | + | -1 | = | -442 | ||
| -147 | + | -3 | = | -150 | ||
| -63 | + | -7 | = | -70 | ||
| -49 | + | -9 | = | -58 | ||
| -21 | + | -21 | = | -42 | ||
| -9 | + | -49 | = | -58 | ||
| -7 | + | -63 | = | -70 | ||
| -3 | + | -147 | = | -150 | ||
| -1 | + | -441 | = | -442 | ||
| 1 | + | 441 | = | 442 | ||
| 3 | + | 147 | = | 150 | ||
| 7 | + | 63 | = | 70 | ||
| 9 | + | 49 | = | 58 | ||
| 21 | + | 21 | = | 42 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 21 and 21
49y2 + 21y + 21y + 9
Step-4 : Add up the first 2 terms, pulling out like factors :
7y • (7y+3)
Add up the last 2 terms, pulling out common factors :
3 • (7y+3)
Step-5 : Add up the four terms of step 4 :
(7y+3) • (7y+3)
Which is the desired factorization
Multiplying Exponential Expressions :
2.2 Multiply (7y+3) by (7y+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (7y+3) and the exponents are :
1 , as (7y+3) is the same number as (7y+3)1
and 1 , as (7y+3) is the same number as (7y+3)1
The product is therefore, (7y+3)(1+1) = (7y+3)2
Final result :
(7y + 3)2
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