Answer:
Sum of cubes identity should be used to prove 35 =3+27
Step-by-step explanation:
Prove that : 35 = 8 +27
Polynomial identities are just equations that are true, but identities are particularly useful for showing the relationship between two apparently unrelated expressions.
Sum of the cubes identity:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
Take RHS
8+ 27
We can write 8 as [tex]2 \times 2 \times 2 = 2^3[/tex] and 27 as [tex]3 \times 3 \times 3 = 3^3[/tex].
then;
8+27 = [tex]2^3+3^3[/tex]
Now, use the sum of cubes identity;
here a =2 and b = 3
[tex]2^3+3^3 = (2+3)(2^2-2\cdot 3+3^2)[/tex]
or
[tex]2^3+3^3 = (5)(4-6+9)[/tex] [tex]= 5 \cdot 7 = 35[/tex] = LHS proved!
therefore, the Sum of cubes polynomial identity should be used to prove that 35 = 8 +27
