153k views
5 votes
23^3 (-12)^3 +(-11)^3 without actually calculating cubes

User Csmba
by
7.8k points

1 Answer

7 votes

Answer:

9108

Explanation:

23^3+(-12)^3+(-11)^3 remove parentheses

= 23^3-12^3-11^3 group difference of two cubes

= (23-12)(23^2+23*12+12^2) + 11^3 factor difference of two cubes

= 11 (23^2+23*12+12^2-11^2) factor ou 11

= 11(23(23+12) + (12+11)(12-11)) apply difference of two squares

= 11 (23*35+23*1) factor out 23

= 11(23*(35+1)) simplify

= 11*23*36 convert 11*23 into difference of 2 squares

= (17^2-6^2)*6^2 expand parentheses

= 102^2-36^2 evaluate squares

= 10404 - 1296 subtraction

= 9108

(no calculator required)

User Tabares
by
7.6k points