factorise : a-8ab^3 factories this sum
Answers
Answer:
Final result :
-a • (2b - 1) • (4b2 + 2b + 1)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
a - 23ab3
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
a - 8ab3 = -a • (8b3 - 1)
Trying to factor as a Difference of Cubes:
3.2 Factoring: 8b3 - 1
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 : 1 is the cube of 1
Check : b3 is the cube of b1
Factorization is :
(2b - 1) • (4b2 + 2b + 1)
Trying to factor by splitting the middle term
3.3 Factoring 4b2 + 2b + 1
The first term is, 4b2 its coefficient is 4 .
The middle term is, +2b its coefficient is 2 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 4 • 1 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 2 .
-4 + -1 = -5 -2 + -2 = -4 -1 + -4 = -5 1 + 4 = 5 2 + 2 = 4 4 + 1 = 5
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-a • (2b - 1) • (4b2 + 2b + 1)