Question

What polynomial identity will prove that 49 = (2+5)^2? (A. Difference of Squares; B. Difference of Cubes; C. Sum of Cubes; D. Square of a Binomial)

Answer 1

Hi,

(a+b)² = a²+2ab+b²

For a = 2 and b = 5

(2+5)² = 2²+2(2)(5)+5²
(2+5)² = 4+20+25
(2+5)² = 49

Answer:

D. Square of a Binomial

Answer 2

Answer:

Option D is correct.

Square of binomials.

Step-by-step explanation:

Prove that: $49 = (2+5)^2$

Square of binomials states that the square of a binomial is always a trinomial.  

Also, it will be helpful to memorize these patterns for writing squares of binomials as trinomials.

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

Take RHS

$(2+5)^2$

Apply the square of binomial, we have;

$(2+5)^2 = 2^2+2 \cdot 2 \cdot 5 +5^2$

                   = 4 + 20 + 25 = 24 + 25 = 49 = LHS           proved.

Therefore, Square of binomials identity will prove that  $49 = (2+5)^2$