Factorise 27y^3+125z^3
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=(3y+5z)(9y^2+25^2-15yz)
Answer:
(3x + 5z) (9x^2 -15zx + 25z^2)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(27 • (x3)) + 53z3
STEP
2
:
Equation at the end of step
2
:
33x3 + 53z3
STEP
3
:
Trying to factor as a Sum of Cubes:
3.1 Factoring: 27x3+125z3
Theory : A sum 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 : z3 is the cube of z1
Factorization is :
(3x + 5z) • (9x2 - 15xz + 25z2)