Question

the volume of a cubical solid is given by following expressions.find the side of field.
a)8a^3+b^3+12a^2 b+6ab^2.

b)27-125a^3-135a+225a^2.

c)27a^3-1/216-9a^2/2+a/4.

d)x^3-1/x63-3x+3/x.
plz help me till 2 o'clock...

Answer 1

8a^3+b^3+12a^2 b+6ab^2
Factor into a cube using the identity:

(x+y)^3 = x^3+3x^2y+3xy^2+y^3
a)8a^3+b^3+12a^2 b+6ab^2.
can be factorized into (2a+b)^3

for b)27-125a^3-135a+225a^2.
note the terms 27 and -125a^3 are perfect cubes, which gives you the hints
27=3^3, -125a^3=(-5a)^3

27a^3-1/216-9a^2/2+a/4.
again, 27a^3=(3a)^3, and 1/216=(1/6)^3

d)x^3-1/x63-3x+3/x.
is probably a typo, should read:
d)x^3-1/x^3-3x+3/x.
Again, use -1/x^3=(-1/x)^3 and x^3

now use the identity.