8x24-27y6 Final result :
(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
Step by step solution :
Step 1 :Skip Ad
Equation at the end of step 1 : (8 • (x24)) - 33y6
Step 2 :Equation at the end of step 2 : 23x24 - 33y6
Step 3 :Trying to factor as a Difference of Squares :
3.1 Factoring: 8x24-27y6
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 : 8 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:
3.2 Factoring: 8x24-27y6
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 : x24 is the cube of x8
Check : y6 is the cube of y2
Factorization is :
(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
Trying to factor as a Difference of Squares :
3.3 Factoring: 2x8 - 3y2
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor a multi variable polynomial :
3.4 Factoring 4x16 + 6x8y2 + 9y4
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
