Question

1 What polynomial identity should be used to prove that 25^2 = (20 + 5)^2 . 2 What polynomial identity should be used to prove that 16^2 = (10 + 6)^2. Possible Answers :. Difference of Cubes. . Difference of Squares. . Square of Binomial. . Sum of Cubes

Answer 1

Answer

The polynomial identity should be used be Square of Binomial.

To prove

Definition of the Square of binomial

A  square binomial is a trinomial that when factored gives you the square of a binomial.

For example, the trinomial x^2 + 2xy + y^2 is a perfect square binomial because it factors to (x + y)^2

$The\ trinomial\ x^{2} +2xy + y^{2}is\ a\ perfect\ square\ binomial\ because\ it\ factors\ to\ (x + y)^2.$

As given

$25^2 = (20 + 5)^2$

It is written as the trimonial

$25^2 = (20^{2} + 5^2 +2\times 20\times 5)$

$625= (400 + 25 +200)$

$625= 625$

Also

16^2 = (10 + 6)^2

It is written as the trimonial

$16^2 = (10^{2} + 6^2 +2\times 10\times 6)$

$256 = (100+ 36 +120)$

$256 = 256$

Therefore the Correct answer is  Square of Binomial.

Answer 2

The answer for the first question is Square of a Binomial because the two terms of the binomial inside the parentheses is equal to 25. The same can be said for the second question because 10 and 6 would also sum up to 16.