4. 9a(6a - 56) – 12a2 (6a - 5b)
Answers
Answer:
9a(6a-5b) -12a²(6a-5b)
(9a- 12a²) (6a-5b).
taking 6a-5b as a common..
=3a(3-4a)(6a-5b).
taking 3a as a common factor if the quadratic 9a-12a²
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9a(6a-5b)-12a2(6a-5b)
Final result :
-3a • (6a - 5b) • (4a - 3)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(9a • (6a - 5b)) - ((22•3a2) • (6a - 5b))
Step 2 :
Equation at the end of step 2 :
(9a • (6a - 5b)) - (22•3a2) • (6a - 5b)
Step 3 :
Equation at the end of step 3 :
9a • (6a - 5b) - (22•3a2) • (6a - 5b)
Step 4 :
Pulling out like terms :
4.1 Pull out 6a-5b
After pulling out, we are left with :
(6a-5b) • ( 9a * 1 +( 22 • 3a2 * (-1) ))
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
9a - 12a2 = -3a • (4a - 3)
Final result :
-3a • (6a - 5b) • (4a - 3)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(9a • (6a - 5b)) - (((22•3a12) • a) • (6a - 5b))
Step 2 :
Equation at the end of step 2 :
(9a • (6a - 5b)) - (22•3a13) • (6a - 5b)
Step 3 :
Equation at the end of step 3 :
9a • (6a - 5b) - (22•3a13) • (6a - 5b)
Step 4 :
Pulling out like terms :
4.1 Pull out 6a-5b
After pulling out, we are left with :
(6a-5b) • ( 9a * 1 +( 22 • 3a13 * (-1) ))
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
9a - 12a13 = -3a • (4a12 - 3)
Trying to factor as a Difference of Squares :
5.2 Factoring: 4a12 - 3
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 4 is the square of 2
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Trying to factor as a Difference of Cubes:
5.3 Factoring: 4a12 - 3
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 : 4 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result :
-3a • (6a - 5b) • (4a12 - 3)