Final result :
-4x40 - 40x - 175
—————————————————
5
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x4" was replaced by "x^4".
(2): ".8" was replaced by "(8/10)".
Step by step solution :
Step 1 :
4
Simplify —
5
Equation at the end of step 1 :
4
((0 - (— • x40)) - 8x) - 35
5
Step 2 :
Equation at the end of step 2 :
4x40
((0 - ————) - 8x) - 35
5
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
8x 8x • 5
8x = —— = ——————
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 :
3.2 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:
-4x40 - (8x • 5) -4x40 - 40x
———————————————— = ———————————
5 5
Equation at the end of step 3 :
(-4x40 - 40x)
————————————— - 35
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 5 as the denominator :
35 35 • 5
35 = —— = ——————
1 5
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
-4x40 - 40x = -4x • (x39 + 10)
Trying to factor as a Sum of Cubes :
5.2 Factoring: x39 + 10
Theory : A sum 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 : 10 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
-4x • (x39+10) - (35 • 5) -4x40 - 40x - 175
————————————————————————— = —————————————————
5 5
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-4x40 - 40x - 175 = -1 • (4x40 + 40x + 175)
Final result :
-4x40 - 40x - 175
—————————————————
5