factorize
8p³+12÷5p²+6÷25p+1÷125
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Changes made to your input should not affect the solution:
(1): "p2" was replaced by "p^2". 1 more similar replacement(s).
STEP1:
1 Simplify ——— 125
Equation at the end of step1:
12 6 1 (((8•(p3))+(——•(p2)))+(——•p))+——— 5 25 125
STEP2:
6 Simplify —— 25
Equation at the end of step2:
12 6 1 (((8•(p3))+(——•(p2)))+(——•p))+——— 5 25 125
STEP 3 :
12 Simplify —— 5
Equation at the end of step3:
12 6p 1 (((8•(p3))+(——•p2))+——)+——— 5 25 125
STEP4:Equation at the end of step 4
12p2 6p 1 (((8 • (p3)) + ————) + ——) + ——— 5 25 125
STEP 5 :
Equation at the end of step5:
12p2 6p 1 ((23p3 + ————) + ——) + ——— 5 25 125
STEP6:Rewriting the whole as an Equivalent Fraction
6.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 5 as the denominator :
23p3 23p3 • 5 23p3 = ———— = ———————— 1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
23p3 • 5 + 12p2 40p3 + 12p2 ——————————————— = ——————————— 5 5
Equation at the end of step6:
(40p3 + 12p2) 6p 1 (————————————— + ——) + ——— 5 25 125
STEP7:
STEP8:Pulling out like terms
8.1 Pull out like factors :
40p3 + 12p2 = 4p2 • (10p + 3)
Calculating the Least Common Multiple :
8.2 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 25
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 5122 Product of all
Prime Factors 52525
Least Common Multiple:
25
Calculating Multipliers :
8.3 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 1
Making Equivalent Fractions :
8.4 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 4p2 • (10p+3) • 5 —————————————————— = ————————————————— L.C.M 25 R. Mult. • R. Num. 6p —————————————————— = —— L.C.M 25
Adding fractions that have a common denominator :
8.5 Adding up the two equivalent fractions
4p2 • (10p+3) • 5 + 6p 200p3 + 60p2 + 6p —————————————————————— = ————————————————— 25 25
Equation at the end of step8:
(200p3 + 60p2 + 6p) 1
Final result :
(10p + 1)3 ---125
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