Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - (2•3a2)) - 25a) - 25
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-6a2 - 25a - 25 = -1 • (6a2 + 25a + 25)
Trying to factor by splitting the middle term
3.2 Factoring 6a2 + 25a + 25
The first term is, 6a2 its coefficient is 6 .
The middle term is, +25a its coefficient is 25 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 6 • 25 = 150
Step-2 : Find two factors of 150 whose sum equals the coefficient of the middle term, which is 25 .
| -150 | + | -1 | = | -151 | ||
| -75 | + | -2 | = | -77 | ||
| -50 | + | -3 | = | -53 | ||
| -30 | + | -5 | = | -35 | ||
| -25 | + | -6 | = | -31 | ||
| -15 | + | -10 | = | -25 | ||
| -10 | + | -15 | = | -25 | ||
| -6 | + | -25 | = | -31 | ||
| -5 | + | -30 | = | -35 | ||
| -3 | + | -50 | = | -53 | ||
| -2 | + | -75 | = | -77 | ||
| -1 | + | -150 | = | -151 | ||
| 1 | + | 150 | = | 151 | ||
| 2 | + | 75 | = | 77 | ||
| 3 | + | 50 | = | 53 | ||
| 5 | + | 30 | = | 35 | ||
| 6 | + | 25 | = | 31 | ||
| 10 | + | 15 | = | 25 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 10 and 15
6a2 + 10a + 15a + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
2a • (3a+5)
Add up the last 2 terms, pulling out common factors :
5 • (3a+5)
Step-5 : Add up the four terms of step 4 :
(2a+5) • (3a+5)
Which is the desired factorization
Final result :
(-3a - 5) • (2a + 5)
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