One edge of a painting is 6 in. longer than the other edge. The picture has a 2-inch-wide frame. Write a quadratic function f in standard form to represent the total area of the picture and frame. Then find the total area of the picture and the frame if its longer edge is 14 inches long.

3x + 4y -25 =0 represents the amount of change sianna should recieve

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)

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1