Question

What polynomial identity should be used to prove that 16^2=(10+6)^2? (A. Difference of Cubes; B. Difference of Squares; C. Square of Binomial; D. Sum of Cubes)

Answer 1

not difference of cubes since it is 2nd degree
not difference of squares since it is plus
not sum of cubes because 2nd degreee

answer is square of binomial (why do we even need this property, oh well)


C

Answer 2

C. Square of Binomial

Explanation:

To prove the identity you should use square of Binomial that states the following:

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

Lets prove it, so first take the equation to solve:

`(10+6)^(2)`

Then square the first term:

`(10+6)^(2)=10^(2)`

Then multiply by 2 the first and second terms:

`(10+6)^(2)=10^(2)+2(10)(6)`

Finally square the second term:

`(10+6)^(2)=10^(2)+2(10)(6)+6^(2)`

Solve the values:

`(10+6)^(2)=100+2(10)(6)+6^(2)`

`(10+6)^(2)=100+120+6^(2)`

`(10+6)^(2)=100+120+36`

`(10+6)^(2)=256`

And prove the polynomial identity:

`16^(2)=256`