Kaia rewrote the sum 96+12 as !2(8+1). She used the same method to rewrite the sum 95+15 as 5(19+3). Describe her method and tell whether she can use it to rewrite the sum 38+11.

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

here's a poem i finished a while ago. i hope you like it and that it inspires you.

=

x=0.8898305 is the answer to that equation