1.what is the simplified form of the following expression? 7m^2+6.5n-4n+2.5m^2-n a. 9.5m^2+1.5n b. 4.5m^2+1.5n c. 1.5m^2-4.2n d. 9.5m^2-1.5n 2.simplify the following expression 1/4(16-12x) a.4+3x b.4-3x c.4+3 d.4-3 3.what is the sum? 7/3+(-3/8) a.65/24 b.47/24 c.-4/5 d.-5/4

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)