In algebra, factoring is the process of finding the factors that multiply together to give you a specific expression. In this case, we are looking to factor the expression A2 – 121. Factoring is an essential skill in algebra that can simplify equations and make them easier to work with.
Understanding Factoring
Factoring is the opposite of expanding. When we expand an expression, we multiply out the terms to get a more complicated expression. Factoring, on the other hand, helps us simplify an expression by breaking it down into its component parts.
When factoring an expression, we are looking for numbers or variables that, when multiplied together, give us the original expression. Factors are like puzzle pieces that fit together to give us the full picture.
Factors of 121
Before we can factor the expression A2 – 121, we need to understand the factors of 121. Factors are numbers that can be multiplied together to give a specific number. In this case, 121 has the following factors:
- 1 and 121
- 11 and 11
This means that 121 can be expressed as the product of 1 and 121, or as the product of 11 and 11.
Factored Form of A2 – 121
Now that we know the factors of 121, we can proceed to factor the expression A2 – 121. To do this, we need to recognize that the original expression is a difference of squares. The difference of squares formula is:
a2 – b2 = (a + b)(a – b)
In this case, A2 – 121 can be written as:
A2 – 121 = A2 – 112
Using the difference of squares formula, we can factor this expression as:
A2 – 121 = (A + 11)(A – 11)
Therefore, the factored form of A2 – 121 is (A + 11)(A – 11).
Application of Factoring
Factoring is a powerful tool in algebra that can be applied in various contexts. Some common applications of factoring include:
- Simplifying Equations: Factoring can simplify complex equations and make them easier to solve.
- Finding Solutions: Factoring can help us find solutions to equations by breaking them down into manageable parts.
- Graphing Functions: Factoring can help us identify the x-intercepts of a function by factoring the expression and setting it equal to zero.
Conclusion
In conclusion, factoring is a useful technique in algebra that can help us simplify expressions and solve equations. In the case of A2 – 121, we can factor the expression using the difference of squares formula to get (A + 11)(A – 11). Understanding factoring and its applications can enhance our problem-solving skills and make algebra more manageable.
