Question

What polynomial identity should be used to prove that 21 = 25 − 4

Answer 1

Choices:
A: Difference of cubes
B: Difference of Squares
C: Square of Binomial
D: Sum of Cubes

The polynomial identity used is B. DIFFERENCE OF SQUARES

21 = 25 - 4
21 = 5² - 2²

Answer 2

the complete question is

What polynomial identity should be used to prove that 21 = 25 − 4

A: Difference of cubes

B: Difference of Squares

C: Square of Binomial

D: Sum of Cubes

we know that

The difference of two squares is a squared number subtracted from another squared number

So

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

In this problem

`image`

then

`(5^(2) -2^(2) )=(5+2)*(5-2)`

`(5^(2) -2^(2) )=(7)*(3)`

`(5^(2) -2^(2) )=21`

`25-4=21`

therefore

the answer is the option

B: Difference of Squares