factorise 1000x^3-1
Answers
Answered by
0
Step-by-step explanation:
1000
x
3
−
1
=
(
10
x
−
1
)
(
100
x
2
+
10
x
+
1
)
Explanation:
Note that both
1000
x
3
=
(
10
x
)
3
and
1
=
1
3
are perfect cubes.
So we can immediately use the difference of cubes identity:
A
3
−
B
3
=
(
A
−
B
)
(
A
2
+
A
B
+
B
2
)
to find:
1000
x
3
−
1
=
(
10
x
)
3
−
1
3
1000
x
3
−
1
=
(
10
x
−
1
)
(
(
10
x
)
2
+
10
x
+
1
)
1000
x
3
−
1
=
(
10
x
−
1
)
(
100
x
2
+
10
x
+
1
)
Answered by
1
Answer:
1000 x 3 − 1 = ( 10 x − 1 ) ( 100 x 2 + 10 x + 1 )
Explanation:
Note that both 1000 x 3 = ( 10 x ) 3 and 1= 1 3 are perfect cubes.
So we can immediately use the difference of cubes identity:
A 3 − B 3 = ( A − B ) ( A 2+ A B + B 2 )
to find:
1000 x 3 − 1 = ( 10 x ) 3 −1 3
1000 x 3 − 1 = ( 10 x − 1 ) ( ( 10 x ) 2 + 10 x + 1 )
1000 x 3 − 1 = ( 10 x−1 ) ( 100 x 2 + 10 x + 1 )
Step-by-step explanation:
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