Given that 2^a×3^b×5^13=20^d×18^12, where a, b, and d are postive integers, compute a+b+d.

75

Step-by-step explanation:

⇒

⇒

⇒

Now compare the like bases:

⇒ A = 2D + 12

⇒ B = 24

⇒ D = 13

Next, let's solve for A:

A = 2D + 12

  = 2(13) + 12

  = 26 + 12

  = 38

LAST STEP: Find the sum of A, B, and D

S = A + B + D

  = 38 + 24 + 13

  = 75

41*67/2=1373.5

step-by-step explanation:

i just used a calculator

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)