Respuesta :
Answer:
Difference of cubes.
Step-by-step explanation:
We are asked to find the identify that will prove that [tex]117=125-8[/tex].
Polynomial identities are equations that are true and have general applications in our algebra work.
We can see that 125 equals [tex]5^3[/tex] and 8 equals [tex]2^3[/tex]. So polynomial identity used in our given problem is difference of cubes.
Difference of cubes: [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Let us prove that 117=125-8.
We can write right hand side of our given equation as:
[tex]5^3-2^3=(5-2)(5^2+5\times 2+2^2)[/tex]
[tex]125-8=(3)(25+10+4)[/tex]
[tex]117=(3)(39)[/tex]
[tex]117=117[/tex]
We can see that left hand side of our equation is equal to right hand side of equation. Hence, proved that difference of cubes will prove our equation equal.
