factorise:-250xy^3-16x^4
Answers
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Factoring multivariable polynomials
Enter an equation or a problem16x4−250xy3
ClearSolve
We think you wrote:
16x^4-250xy^3
This deals with factoring multivariable polynomials.
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1 result(s) found
2x⋅(2x−5y)⋅(4x2+10xy+25y2)
See steps
Step by Step Solution:
STEP1:Equation at the end of step 1 (16 • (x4)) - (2•53xy3) STEP 2 :Equation at the end of step2: 24x4 - (2•53xy3) STEP3:STEP4:Pulling out like terms
4.1 Pull out like factors :
16x4 - 250xy3 = 2x • (8x3 - 125y3)
Trying to factor as a Difference of Cubes:
4.2 Factoring: 8x3 - 125y3
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 : 125 is the cube of 5
Check : x3 is the cube of x1
Check : y3 is the cube of y1
Factorization is :
(2x - 5y) • (4x2 + 10xy + 25y2)
Trying to factor a multi variable polynomial :
4.3 Factoring 4x2 + 10xy + 25y2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
2x • (2x - 5y) • (4x2 + 10xy + 25y2)
Terms and topics
Factoring multivariable polynomialsMultiplying exponentsFactoring binomials as sum or difference of cubes
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