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Sandy
20 October, 04:45
What is the factored form of 8x^24-27y^6
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Lance
20 October, 04:52
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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)
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Amare
20 October, 08:44
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The answer will be (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
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