Find the value of x
3
−
x
3
1
when x−
x
1
=5.
- A150
- B125
- C140
- D100
Solution & Step-by-step Explanation
Given:
x−
x
1
=5
Using the algebraic identity for the cube of a binomial difference:
(x−
x
1
)
3
=x
3
−
x
3
1
−3⋅x⋅
x
1
(x−
x
1
)
(x−
x
1
)
3
=x
3
−
x
3
1
−3(x−
x
1
)
Substituting the given value x−
x
1
=5:
5
3
=x
3
−
x
3
1
−3(5)
125=x
3
−
x
3
1
−15
x
3
−
x
3
1
=125+15=140
x−
x
1
=5
Using the algebraic identity for the cube of a binomial difference:
(x−
x
1
)
3
=x
3
−
x
3
1
−3⋅x⋅
x
1
(x−
x
1
)
(x−
x
1
)
3
=x
3
−
x
3
1
−3(x−
x
1
)
Substituting the given value x−
x
1
=5:
5
3
=x
3
−
x
3
1
−3(5)
125=x
3
−
x
3
1
−15
x
3
−
x
3
1
=125+15=140