Question

Which polynomial identity will prove that 16 = 25 − 9?

Difference of Squares
Difference of Cubes
Sum of Cubes
Square of a Binomial

Answer 1

Difference of Squares

Answer 2

Answer: Difference of Squares

Explanation:

Since, According to the polynomial identity of the Difference of Squares,

If a and b are two numbers or polynomials then we can write,

`a^2 - b^2 = (a+b) (a-b)`

Here our expression,

16 = 25 − 9

Since, we can write,

`25 - 9 = 5^2 - 3^2`

⇒
`25 - 9 = (5+3)* (5-3)` ( By applying polynomial identity of Difference of Squares )

⇒
`25 - 9 = 8* 2`

⇒
`25 - 9 = 16`

Hence proved.