Factorise: 54x^3y-128y4
Answers
Hi,
here u go with ur answer...
STEP
1
:
Equation at the end of step 1
((54 • (x3)) • y) - 27y4
STEP
2
:
Equation at the end of step
2
:
((2•33x3) • y) - 27y4
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
54x3y - 128y4 = 2y • (27x3 - 64y3)
Trying to factor as a Difference of Cubes:
4.2 Factoring: 27x3 - 64y3
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 : 27 is the cube of 3
Check : 64 is the cube of 4
Check : x3 is the cube of x1
Check : y3 is the cube of y1
Factorization is :
(3x - 4y) • (9x2 + 12xy + 16y2)
Trying to factor a multi variable polynomial :
4.3 Factoring 9x2 + 12xy + 16y2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
2y • (3x - 4y) • (9x2 + 12xy +16y²)
Mark the answer as BRAINLIEST