How to find the difference of two squares

Understand the Problem

The question is asking how to identify or calculate the difference between two squared numbers using the mathematical property known as the difference of squares.

Answer

The difference of squared numbers can be calculated as $a^2 - b^2 = (a - b)(a + b)$. For example, $5^2 - 3^2 = 16$.

Steps to Solve

Identify the Squared Numbers

To apply the difference of squares formula, we need two squared numbers. Let's represent them as $a^2$ and $b^2$.

State the Difference of Squares Formula

The difference of squares can be expressed by the formula: $$ a^2 - b^2 = (a - b)(a + b) $$

This means that if we can find $a$ and $b$, we can quickly calculate the difference.

Substitute the Values

Once you have identified what $a$ and $b$ are, substitute those values into the difference of squares formula. For example, if $a = 5$ and $b = 3$, it becomes: $$ 5^2 - 3^2 = (5 - 3)(5 + 3) $$

Calculate the Results

Perform the subtraction and addition:

First calculate $5 - 3 = 2$ and $5 + 3 = 8$.
Then multiply the results: $$ (5 - 3)(5 + 3) = 2 \times 8 = 16 $$

Verify the Calculation

Finally, verify the result by calculating $5^2 - 3^2$ directly: $$ 5^2 = 25 \quad \text{and} \quad 3^2 = 9 $$

Now calculate the difference: $$ 25 - 9 = 16 $$

This confirms that the calculation is correct.

The difference of two squared numbers is calculated using the formula: $$ a^2 - b^2 = (a - b)(a + b) $$

For example, the difference for $5^2 - 3^2$ is $16$.

More Information

The difference of squares formula is a powerful algebraic tool that simplifies the calculation of the difference between two squared numbers, which can often seem complex at first glance.

Tips

Forgetting to correctly calculate $a - b$ and $a + b$.
Mislabeling $a$ and $b$ or using incorrect values.
Confusing the difference of squares formula with other formulas, such as the square of a binomial.

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