Factorise: 32a3 + 108b3
Answers
Answer:
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Step-by-step explanation:
32a3+108b3
Final result :
4 • (2a + 3b) • (4a2 - 6ab + 9b2)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "b3" was replaced by "b^3". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(32 • (a3)) + (22•33b3)
Step 2 :
Equation at the end of step 2 :
25a3 + (22•33b3)
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
32a3 + 108b3 = 4 • (8a3 + 27b3)
Trying to factor as a Sum of Cubes :
4.2 Factoring: 8a3 + 27b3
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 : 8 is the cube of 2
Check : 27 is the cube of 3
Check : a3 is the cube of a1
Check : b3 is the cube of b1
Factorization is :
(2a + 3b) • (4a2 - 6ab + 9b2)
Trying to factor a multi variable polynomial :
4.3 Factoring 4a2 - 6ab + 9b2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
4 • (2a + 3b) • (4a2 - 6ab + 9b2)
Answer:
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