Final answer:
To square 26 without a calculator, we can rewrite 26 as the sum of 20 and 6, then apply the identity (x − y)² = x² − 2xy + y², with x being 20 and y being -6, resulting in 676. None of the options provided matches this method.
Step-by-step explanation:
The question is about using the algebraic identity (x − y)² = x² − 2xy + y² to square the number 26. This identity states that the square of the difference of two numbers x and y equals the square of x minus twice the product of x and y plus the square of y.
To square 26 using this identity, we can write 26 as (20 + 6) and apply the identity with x being 20 and y being -6:
(26)² = (20 + 6)²
= (20)² + 2*(20)*(6) + (-6)²
= 400 + 240 + 36
= 676.
So the answer is 676, and none of the options given (A, B, C, or D) correctly represents this process.