Solution - Simplification or other simple results
Other Ways to Solve
Simplification or other simple resultsStep by Step Solution
0 p7_Paren_Max_Level 0 1 p7_Total_i 0 2 p7_Level_1_i 0 3 p7_N_Level_1_Close_Paren 2 4 p7_N_Commas 0 5 p7_Total_Dots 0 6 p7_Level_z_dots 0 7 p7_Level_1_dots 0 8 p7_GT_LT 0 9 p7_var_after_non_al 8 10 p7_First_Non_Alpha 0 11 p7_EQ 0 12 p7_Numbers 16 13 p7_Dot_in_Numbers 0 14 p7_Dot_Outside_Numbers 0 15 p7_Semi_Col 0 16 p7_Errors 0 17 p7_Total_Ops 11 18 p7_Lvl_One_Ops 2 19 p7_Lvl_One_P_M 0 20 p7_LCM_GCF_FOUND 0 21 p7_Area 0 22 p7_sqrt_found 0 23 p7_close_open_paren 0 24 p7_factor_or_prime 0 25 p7_vars 8 26 p7_kova_2 0 27 p7_var_2 0 28 p7_product_of_vars 0 29 p7_sqrt_error 0 30 p7_unallowed_ops_in sqrt +/: 0
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "p2" was replaced by "p^2". 3 more similar replacement(s).
Step 1 :
Equation at the end of step 1 :
(((14•(p2))+17p)+5) (((2•(p2))+9p)+4) ———————————————————— ÷ ————————————————— (((20•(p2))+19p)-28) ((22p2+23p)+28)Step 2 :
Equation at the end of step 2 :
(((14•(p2))+17p)+5) ((2p2+9p)+4)
———————————————————— ÷ ————————————
(((20•(p2))+19p)-28) (4p2+23p+28)
Step 3 :
2p2 + 9p + 4
Simplify ——————————————
4p2 + 23p + 28
Trying to factor by splitting the middle term
3.1 Factoring 2p2 + 9p + 4
The first term is, 2p2 its coefficient is 2 .
The middle term is, +9p its coefficient is 9 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 2 • 4 = 8
Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is 9 .
| -8 | + | -1 | = | -9 | ||
| -4 | + | -2 | = | -6 | ||
| -2 | + | -4 | = | -6 | ||
| -1 | + | -8 | = | -9 | ||
| 1 | + | 8 | = | 9 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 8
2p2 + 1p + 8p + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (2p+1)
Add up the last 2 terms, pulling out common factors :
4 • (2p+1)
Step-5 : Add up the four terms of step 4 :
(p+4) • (2p+1)
Which is the desired factorization
Trying to factor by splitting the middle term
3.2 Factoring 4p2+23p+28
The first term is, 4p2 its coefficient is 4 .
The middle term is, +23p its coefficient is 23 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 4 • 28 = 112
Step-2 : Find two factors of 112 whose sum equals the coefficient of the middle term, which is 23 .
| -112 | + | -1 | = | -113 | ||
| -56 | + | -2 | = | -58 | ||
| -28 | + | -4 | = | -32 | ||
| -16 | + | -7 | = | -23 | ||
| -14 | + | -8 | = | -22 | ||
| -8 | + | -14 | = | -22 | ||
| -7 | + | -16 | = | -23 | ||
| -4 | + | -28 | = | -32 | ||
| -2 | + | -56 | = | -58 | ||
| -1 | + | -112 | = | -113 | ||
| 1 | + | 112 | = | 113 | ||
| 2 | + | 56 | = | 58 | ||
| 4 | + | 28 | = | 32 | ||
| 7 | + | 16 | = | 23 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 16
4p2 + 7p + 16p + 28
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (4p+7)
Add up the last 2 terms, pulling out common factors :
4 • (4p+7)
Step-5 : Add up the four terms of step 4 :
(p+4) • (4p+7)
Which is the desired factorization
Canceling Out :
3.3 Cancel out (p+4) which appears on both sides of the fraction line.
Equation at the end of step 3 :
(((14•(p2))+17p)+5) (2p+1) ———————————————————— ÷ —————— (((20•(p2))+19p)-28) 4p+7Step 4 :
Equation at the end of step 4 :
(((14•(p2))+17p)+5) (2p+1) ——————————————————— ÷ —————— (((22•5p2)+19p)-28) 4p+7Step 5 :
Equation at the end of step 5 :
(((2•7p2) + 17p) + 5) (2p + 1)
————————————————————— ÷ ————————
(20p2 + 19p - 28) 4p + 7
Step 6 :
14p2 + 17p + 5
Simplify ———————————————
20p2 + 19p - 28
Trying to factor by splitting the middle term
6.1 Factoring 14p2 + 17p + 5
The first term is, 14p2 its coefficient is 14 .
The middle term is, +17p its coefficient is 17 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 14 • 5 = 70
Step-2 : Find two factors of 70 whose sum equals the coefficient of the middle term, which is 17 .
| -70 | + | -1 | = | -71 | ||
| -35 | + | -2 | = | -37 | ||
| -14 | + | -5 | = | -19 | ||
| -10 | + | -7 | = | -17 | ||
| -7 | + | -10 | = | -17 | ||
| -5 | + | -14 | = | -19 | ||
| -2 | + | -35 | = | -37 | ||
| -1 | + | -70 | = | -71 | ||
| 1 | + | 70 | = | 71 | ||
| 2 | + | 35 | = | 37 | ||
| 5 | + | 14 | = | 19 | ||
| 7 | + | 10 | = | 17 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 10
14p2 + 7p + 10p + 5
Step-4 : Add up the first 2 terms, pulling out like factors :
7p • (2p+1)
Add up the last 2 terms, pulling out common factors :
5 • (2p+1)
Step-5 : Add up the four terms of step 4 :
(7p+5) • (2p+1)
Which is the desired factorization
Trying to factor by splitting the middle term
6.2 Factoring 20p2+19p-28
The first term is, 20p2 its coefficient is 20 .
The middle term is, +19p its coefficient is 19 .
The last term, "the constant", is -28
Step-1 : Multiply the coefficient of the first term by the constant 20 • -28 = -560
Step-2 : Find two factors of -560 whose sum equals the coefficient of the middle term, which is 19 .
| -560 | + | 1 | = | -559 | ||
| -280 | + | 2 | = | -278 | ||
| -140 | + | 4 | = | -136 | ||
| -112 | + | 5 | = | -107 | ||
| -80 | + | 7 | = | -73 | ||
| -70 | + | 8 | = | -62 | ||
| -56 | + | 10 | = | -46 | ||
| -40 | + | 14 | = | -26 | ||
| -35 | + | 16 | = | -19 | ||
| -28 | + | 20 | = | -8 | ||
| -20 | + | 28 | = | 8 | ||
| -16 | + | 35 | = | 19 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 35
20p2 - 16p + 35p - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
4p • (5p-4)
Add up the last 2 terms, pulling out common factors :
7 • (5p-4)
Step-5 : Add up the four terms of step 4 :
(4p+7) • (5p-4)
Which is the desired factorization
Equation at the end of step 6 :
(2p + 1) • (7p + 5) (2p + 1)
——————————————————— ÷ ————————
(5p - 4) • (4p + 7) 4p + 7
Step 7 :
(2p+1)•(7p+5) 2p+1
Divide ————————————— by ——————
(5p-4)•(4p+7) (4p+7)
7.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
(2p + 1) • (7p + 5) 2p + 1 (2p + 1) • (7p + 5) 4p + 7 ——————————————————— ÷ ———————— = ——————————————————— • ———————— (5p - 4) • (4p + 7) (4p + 7) (5p - 4) • (4p + 7) (2p + 1)
Canceling Out :
7.2 Cancel out (2p + 1) which appears on both sides of the fraction line.
Canceling Out :
7.3 Cancel out (4p + 7) which appears on both sides of the fraction line.
Final result :
7p + 5
——————
5p - 4
How did we do?
Please leave us feedback.