16 a to the power 4 - 54 a
Answers
Answer:
2a • (2a - 3) • (4a2 + 6a + 9)
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
24a4 - 54a
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
16a4 - 54a = 2a • (8a3 - 27)
Trying to factor as a Difference of Cubes:
3.2 Factoring: 8a3 - 27
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 : 27 is the cube of 3
Check : a3 is the cube of a1
Factorization is :
(2a - 3) • (4a2 + 6a + 9)
Trying to factor by splitting the middle term
3.3 Factoring 4a2 + 6a + 9
The first term is, 4a2 its coefficient is 4 .
The middle term is, +6a its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 6 .
-36 + -1 = -37
-18 + -2 = -20
-12 + -3 = -15
-9 + -4 = -13
-6 + -6 = -12
-4 + -9 = -13
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!