Solution - Simplification or other simple results
Other Ways to Solve
Simplification or other simple resultsStep by Step Solution
Step 1 :
Equation at the end of step 1 :
(((20•(n2))-31n)+12) (((12•(n2))-n)-6)•———————————————————— (((3•5n2)-2n)-8)Step 2 :
Equation at the end of step 2 :
(((22•5n2)-31n)+12)
(((12•(n2))-n)-6)•———————————————————
(15n2-2n-8)
Step 3 :
20n2 - 31n + 12
Simplify ———————————————
15n2 - 2n - 8
Trying to factor by splitting the middle term
3.1 Factoring 20n2 - 31n + 12
The first term is, 20n2 its coefficient is 20 .
The middle term is, -31n its coefficient is -31 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 20 • 12 = 240
Step-2 : Find two factors of 240 whose sum equals the coefficient of the middle term, which is -31 .
| -240 | + | -1 | = | -241 | ||
| -120 | + | -2 | = | -122 | ||
| -80 | + | -3 | = | -83 | ||
| -60 | + | -4 | = | -64 | ||
| -48 | + | -5 | = | -53 | ||
| -40 | + | -6 | = | -46 | ||
| -30 | + | -8 | = | -38 | ||
| -24 | + | -10 | = | -34 | ||
| -20 | + | -12 | = | -32 | ||
| -16 | + | -15 | = | -31 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and -15
20n2 - 16n - 15n - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
4n • (5n-4)
Add up the last 2 terms, pulling out common factors :
3 • (5n-4)
Step-5 : Add up the four terms of step 4 :
(4n-3) • (5n-4)
Which is the desired factorization
Trying to factor by splitting the middle term
3.2 Factoring 15n2-2n-8
The first term is, 15n2 its coefficient is 15 .
The middle term is, -2n its coefficient is -2 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 15 • -8 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -2 .
| -120 | + | 1 | = | -119 | ||
| -60 | + | 2 | = | -58 | ||
| -40 | + | 3 | = | -37 | ||
| -30 | + | 4 | = | -26 | ||
| -24 | + | 5 | = | -19 | ||
| -20 | + | 6 | = | -14 | ||
| -15 | + | 8 | = | -7 | ||
| -12 | + | 10 | = | -2 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 10
15n2 - 12n + 10n - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
3n • (5n-4)
Add up the last 2 terms, pulling out common factors :
2 • (5n-4)
Step-5 : Add up the four terms of step 4 :
(3n+2) • (5n-4)
Which is the desired factorization
Canceling Out :
3.3 Cancel out (5n-4) which appears on both sides of the fraction line.
Equation at the end of step 3 :
(4n - 3) (((12 • (n2)) - n) - 6) • ———————— 3n + 2Step 4 :
Equation at the end of step 4 :
(4n - 3)
(((22•3n2) - n) - 6) • ————————
3n + 2
Step 5 :
Trying to factor by splitting the middle term
5.1 Factoring 12n2-n-6
The first term is, 12n2 its coefficient is 12 .
The middle term is, -n its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 12 • -6 = -72
Step-2 : Find two factors of -72 whose sum equals the coefficient of the middle term, which is -1 .
| -72 | + | 1 | = | -71 | ||
| -36 | + | 2 | = | -34 | ||
| -24 | + | 3 | = | -21 | ||
| -18 | + | 4 | = | -14 | ||
| -12 | + | 6 | = | -6 | ||
| -9 | + | 8 | = | -1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 8
12n2 - 9n + 8n - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3n • (4n-3)
Add up the last 2 terms, pulling out common factors :
2 • (4n-3)
Step-5 : Add up the four terms of step 4 :
(3n+2) • (4n-3)
Which is the desired factorization
Canceling Out :
5.2 Cancel out (3n+2) which appears on both sides of the fraction line.
Multiplying Exponential Expressions :
5.3 Multiply (4n-3) by (4n-3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (4n-3) and the exponents are :
1 , as (4n-3) is the same number as (4n-3)1
and 1 , as (4n-3) is the same number as (4n-3)1
The product is therefore, (4n-3)(1+1) = (4n-3)2
Final result :
(4n - 3)2
How did we do?
Please leave us feedback.