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:
\(a^3+b^3=(a+b)(a^2-ab+b^2)\)
Take RHS
8+ 27
We can write 8 as \(2 \times 2 \times 2 = 2^3\) and 27 as \(3 \times 3 \times 3 = 3^3\).
then;
8+27 = \(2^3+3^3\)
Now, use the sum of cubes identity;
here a =2 and b = 3
\(2^3+3^3 = (2+3)(2^2-2\cdot 3+3^2)\)
or
\(2^3+3^3 = (5)(4-6+9)\) \(= 5 \cdot 7 = 35\) = LHS proved!
therefore, the Sum of cubes polynomial identity should be used to prove that 35 = 8 +27
