Addition property subtraction property multiplication property division property simplifying distributive property

step-1: Given equation

step-2:

Since, in both sides , there is 7 in the denominator

so, we are dividing both sides by 7

so, division property

step-3:

we can see that 7 is getting cancelled with 7 on left side

and 7 is getting cancelled with -35 on right side

so, we are simplifying it

so, simplifying property

step-4:

we can see that 2 is added  on left side and 2 is added on right side

so, we are adding 2 on both sides

so, addition property

step-5:

we can see that 2 on both sides are no more

it has been added with -2 on left side and -5 on right side

so, it will help in simplification

so, simplifying property

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)