49.6k views
0 votes
Which polynomial identity will prove that 19 = 27 − 8? Difference of Squares Difference of Cubes Sum of Cubes Square of a Binomial

User Jeff Hall
by
8.6k points

2 Answers

4 votes

Answer:

B

Step-by-step explanation:

difference of cubes

User Khawaja Asim
by
8.5k points
3 votes
The correct answer is: [B]: "Difference of Cubes".
__________________________________________________________

Step-by-step explanation:
__________________________________________________________
Note that the equation/identity for the "difference of cubes" is expressed as:
__________________________________________________________

" a
³ − b³ = (a − b)(a² + ab + b²) " ;
__________________________________________________________

Note the given equation: " 19 = 27
− 8 " ; (which is true).
__________________________________________________________

The "right hand side" of this equation:

" 27 − 8 " ; contains two numbers:

"27" and "8" ; both of which are "cubes" ;

→ that is: ∛27 = 3 ; = 3 * 3 * 3 = 9 * 3 = 27 ; and:

∛ 8 = 2 ; 2³ = 2 * 2 * 2 = 4 * 2 = 8 ;

AND: "8" is being SUBTRACTED from "27" ;

(hence, the "difference of squares" polynomial identity);

So: given: " 19 = 27 − 8 " ;

→ Rewrite as:

" 19 = 3³ − 2³ " ;
_______________________________________________________
Now, consider the identity equation for the "difference of squares":

" a³ − b³ = (a − b)(a² + ab + b²) " ;
_______________________________________________________

Take: " 19 = 3³ − 2³ " ;

and rewrite as:

→ 3³ − 2³ = 19 ;

So: (a³ − b³) = 3³ − 2³ ;

a = 3 ; b = 2 ;
___________________________________________________________
Plug in these values:

" a³ − b³ = (a − b)(a² + ab + b²) " ;

− 2³ ≟ [3 − 2) [ 3² + (3*2) + 2² ] ≟ 19 ? ;

27 − 8 (1) (9 + 6 + 4) ≟ 19 ? ;

19 (1) (15 + 4) ≟ 19 ? ;

19 ≟ (1) (19) ≟ 19 ? ;

19 19 ≟ 19 ? ;

19 = 19 = 19 ! Yes!
___________________________________________________________
User Brian Yeh
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories