Answer:
-259dot - 12abc3
————————————————
3abc3
Step-by-step explanation:
Dividing exponential expressions :
a2 divided by a3 = a(2 - 3) = a(-1) = 1/a1 = 1/a
b3 divided by b4 = b(3 - 4) = b(-1) = 1/b1 = 1/b
Equation at the end of step 3: -7
(37 • —————) - 4
3abc3
Rewriting the whole as an Equivalent Fraction:
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3abc3 as the denominator :
4 4 • 3abc3
4 = — = —————————
1 3abc3
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:
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-259dot - (4 • 3abc3) -259dot - 12abc3
————————————————————— = ————————————————
3abc3 3abc3
Pulling out like terms:
Pull out like factors :
-259dot - 12abc3 = -1 • (259dot + 12abc3)
Trying to factor as a Sum of Cubes:
Factoring: 259dot + 12abc3
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 : 259 is not a cube !!
-Hope this helped
