What polynomial identity should be used to prove that 21 = 25 − 4
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
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
\(25=5^{2}\\ 4=2^{2}
\)
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