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3u⁴-24uv³
Please answer my question
Answers
Answer:Step by Step Solution
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STEP
1
:
Equation at the end of step 1
(3 • (u4)) - (23•3uv3)
STEP
2
:
Equation at the end of step
2
:
3u4 - (23•3uv3)
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
3u4 - 24uv3 = 3u • (u3 - 8v3)
Trying to factor as a Difference of Cubes:
4.2 Factoring: u3 - 8v3
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 : u3 is the cube of u1
Check : v3 is the cube of v1
Factorization is :
(u - 2v) • (u2 + 2uv + 4v2)
Trying to factor a multi variable polynomial :
4.3 Factoring u2 + 2uv + 4v2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
3u • (u - 2v) • (u2 + 2uv + 4v2)
Step-by-step explanation: mark mr brainliest