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Show how to use the identity (x − y)² = x² − 2xy + y² to square 26 without using a calculator.

A. (26 - 226 + 26)²
B. (26² - 226 + 26²)
C. (26² - 226 + 1)
D. (26² - 21 + 26²)

User Sleeparrow
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1 Answer

3 votes

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.

User Drew Schuster
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