Question

What polynomial identity should be used to prove that 252 = (20 + 5)2?

Select one:
a. Difference of Cubes
b. Difference of Squares
c. Square of Binomial
d. Sum of Cubes

Answer 1

To prove that 252 equals (20 + 5) squared, we use the Square of a Binomial identity, which upon expansion and simplification confirms that (20 + 5)^2 equals 625.

Step-by-step explanation:

To prove that 252 = (20 + 5)2, the correct polynomial identity to use is the Square of a Binomial. This identity states that the square of a binomial (a + b)2 is equal to a2 + 2ab + b2. By applying this identity, we can expand (20 + 5)2 as follows:

1. Square the first term: 202 = 400.
2. Multiply the first term by the second term and then by 2: 2 × 20 × 5 = 200.
3. Square the second term: 52 = 25.
4. Add these results together: 400 + 200 + 25 = 625.

Therefore, (20 + 5)2 = 625 which confirms our original statement.