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(a-5)^2 - (a+5)^2: A Simplification Guide
In algebra, simplifying expressions involving squared binomials can be a challenging task. One such expression is (a-5)^2 - (a+5)^2. In this article, we will guide you through the steps to simplify this expression.
Step 1: Expand the Squared Binomials
To start, we need to expand each squared binomial using the formula (a+b)^2 = a^2 + 2ab + b^2.
(a-5)^2 = a^2 - 10a + 25 (a+5)^2 = a^2 + 10a + 25
Step 2: Write the Expression
Now, we can write the original expression using the expanded binomials:
(a-5)^2 - (a+5)^2 = (a^2 - 10a + 25) - (a^2 + 10a + 25)
Step 3: Simplify the Expression
Next, we need to simplify the expression by combining like terms:
a^2 - 10a + 25 - a^2 - 10a - 25
Notice that the a^2 terms cancel out, as do the 25 terms. We are left with:
-20a
Therefore, the simplified expression is:
(a-5)^2 - (a+5)^2 = -20a
Conclusion
In conclusion, simplifying the expression (a-5)^2 - (a+5)^2 involves expanding the squared binomials, writing the expression, and combining like terms. The final simplified expression is -20a. This result can be used in various mathematical applications, such as solving equations and inequalities.
