factorise 81x^3 – 375y^3
Answers
Answer:
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Step-by-step explanation:
STEP1:Equation at the end of step 1
(81 • (x3)) - (3•53y3)
STEP 2 :
Equation at the end of step2:
34x3 - (3•53y3)
STEP3:
STEP4:Pulling out like terms
4.1 Pull out like factors :
81x3 - 375y3 = 3 • (27x3 - 125y3)
Trying to factor as a Difference of Cubes:
4.2 Factoring: 27x3 - 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 : 27 is the cube of 3
Check : 125 is the cube of 5
Check : x3 is the cube of x1
Check : y3 is the cube of y1
Factorization is :
(3x - 5y) • (9x2 + 15xy + 25y2
Answer:
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Step-by-step explanation:
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