factorise a 2 b 2

less than a minute read 17-10-2024

Factoring Expressions: Demystifying "a²b²"

Factoring expressions is a fundamental skill in algebra, allowing us to simplify complex equations and solve them more easily. One common expression you might encounter is "a²b²", and understanding how to factor it can be a valuable starting point.

What Does "a²b²" Mean?

Let's break down the components:

a²: This represents "a multiplied by itself" (a * a).
b²: This represents "b multiplied by itself" (b * b).
a²b²: This represents "a multiplied by itself, then multiplied by b multiplied by itself" (a * a * b * b).

Factoring a²b²

To factor "a²b²", we essentially reverse the multiplication process. Here's how:

Identify the common factors: Both "a²" and "b²" share the factors "a" and "b".
Group the factors: We can rearrange the expression as (a * a) * (b * b).
Express as a product: This can be written as (a * b) * (a * b), which simplifies to (ab)²

Therefore, the factored form of a²b² is (ab)².

Practical Applications

Factoring expressions like "a²b²" is essential in various mathematical contexts, including:

Solving equations: Factoring can help simplify equations and isolate variables for easier solutions.
Simplifying expressions: Factoring can reduce complex expressions to more manageable forms.
Algebraic manipulation: Factoring plays a crucial role in various algebraic manipulations, such as simplifying fractions or finding common denominators.

Examples

Let's look at some examples:

Example 1: If a = 2 and b = 3, then a²b² = (2 * 2) * (3 * 3) = 4 * 9 = 36. This can also be calculated directly as (2 * 3)² = 6² = 36.
Example 2: The expression 4x²y² can be factored as (2x)² * (y)² = (2xy)².

Conclusion

Understanding how to factor expressions like "a²b²" is a fundamental step in mastering algebraic concepts. By breaking down the expression into its component parts and recognizing the common factors, we can simplify and manipulate these expressions efficiently.