Question

What polynomial identity should be used to prove that 35 = 8 + 27

Answer 1

Sum of cubes because 27 + 8 = 3^3 + 2^3

Answer 2

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