64x3÷125-96x2÷25-8+48x÷5
Answers
Answer:
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
STEP
1
:
x
Simplify —
5
Equation at the end of step
1
:
(x3) (x2) x
(((64•————)-8)-(96•————))+(48•—)
125 25 5
STEP
2
:
x2
Simplify ——
25
Equation at the end of step
2
:
(x3) x2 48x
(((64•————)-8)-(96•——))+———
125 25 5
STEP
3
:
x3
Simplify ———
125
Equation at the end of step
3
:
x3 96x2 48x
(((64 • ———) - 8) - ————) + ———
125 25 5
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 125 as the denominator :
8 8 • 125
8 = — = ———————
1 125
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 :
4.2 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:
64x3 - (8 • 125) 64x3 - 1000
———————————————— = ———————————
125 125
Equation at the end of step
4
:
(64x3 - 1000) 96x2 48x
(————————————— - ————) + ———
125 25 5
STEP
5
:
STEP
6
:
Pulling out like terms
6.1 Pull out like factors :
64x3 - 1000 = 8 • (8x3 - 125)
Trying to factor as a Difference of Cubes:
6.2 Factoring: 8x3 - 125
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 8 is the cube of 2
Check : 125 is the cube of 5
Check : x3 is the cube of x1
Factorization is :
(2x - 5) • (4x2 + 10x + 25)
Trying to factor by splitting the middle term
6.3 Factoring 4x2 + 10x + 25
The first term is, 4x2 its coefficient is 4 .
The middle term is, +10x its coefficient is 10 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 4 • 25 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is 10 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20
-5 + -20 = -25