To evaluate \( 48^2 \) using identities, we can apply the **square of a binomial** identity:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

We can express 48 as \( 50 - 2 \) to simplify the calculation:

\[
48^2 = (50 - 2)^2
\]

Now, applying the identity:

\[
(50 - 2)^2 = 50^2 - 2 \times 50 \times 2 + (-2)^2
\]

Let's calculate each term:

- \( 50^2 = 2500 \)
- \( 2 \times 50 \times 2 = 200 \)
- \( (-2)^2 = 4 \)

Now, putting everything together:

\[
48^2 = 2500 - 200 + 4 = 2304
\]

So, \( 48^2 = 2304 \).

Would you like more details on the steps? Here are some related questions:

1. How can we apply the same method to other numbers?
2. What other algebraic identities are useful for squaring numbers?
3. How can we generalize this approach for any two-digit number?
4. What are other methods for calculating large squares without a calculator?
5. How can this identity be used in solving quadratic equations?

**Tip**: Breaking numbers into convenient parts can make mental math easier and faster.

Learn how to evaluate 48^2 using the square of a binomial identity. This step-by-step guide simplifies 48 as (50 - 2) and applies the binomial formula (a + b)^2 = a^2 + 2ab + b^2 to calculate the result. Ideal for students in Grades 8-10.

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