Find the squares of each of the following without multiplication. 295

To find the square of \( 295 \) without direct multiplication, you can use the algebraic identity:

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

Here, let \( a = 300 \) and \( b = 5 \), so:

\[
295^2 = (300 - 5)^2
\]

Using the identity:

\[
(300 - 5)^2 = 300^2 - 2(300)(5) + 5^2
\]

Now, calculate each part:

\[
300^2 = 90,000
\]

\[
2(300)(5) = 3,000
\]

\[
5^2 = 25
\]

Putting it all together:

\[
295^2 = 90,000 - 3,000 + 25 = 87,025
\]

So, the square of \( 295 \) is \( 87,025 \).

Would you like any further details or have any questions?

Here are 5 related questions you might consider:
1. How can you square \( 285 \) using the same method?
2. What other algebraic identities can simplify squaring numbers?
3. How would you find the square of \( 305 \) using this approach?
4. Can you use this method for numbers not close to a round number?
5. How does this method compare to direct multiplication in terms of efficiency?

**Tip:** When using algebraic identities, always double-check that your chosen \( a \) and \( b \) values simplify the calculation effectively.

Discover how to find the square of 295 without direct multiplication using algebraic identities. Learn step-by-step with detailed calculations and examples. Suitable for high school students studying algebraic manipulation and advanced arithmetic.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation