(x%2B5)-(x%2B5)%5E2.jpeg "(x-5)(x+5)-(x+5)^2")
Simplifying the Expression (x-5)(x+5)-(x+5)^2
This article will walk you through the steps of simplifying the algebraic expression (x-5)(x+5)-(x+5)^2.
Expanding the Expressions
First, we need to expand both parts of the expression.
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(x-5)(x+5) is a difference of squares pattern. This pattern simplifies to (a-b)(a+b) = a^2 - b^2. Applying this to our expression, we get:
- (x-5)(x+5) = x^2 - 5^2 = x^2 - 25
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(x+5)^2 is a perfect square trinomial. This pattern simplifies to (a+b)^2 = a^2 + 2ab + b^2. Applying this to our expression, we get:
- (x+5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25
Combining the Simplified Expressions
Now that we've expanded both parts of the expression, we can combine them:
(x-5)(x+5)-(x+5)^2 = (x^2 - 25) - (x^2 + 10x + 25)
Simplifying the Expression
To simplify further, we distribute the negative sign:
x^2 - 25 - x^2 - 10x - 25
Now, we combine like terms:
(x^2 - x^2) + (-25 - 25) - 10x = -50 - 10x
Final Simplified Expression
Therefore, the simplified form of the expression (x-5)(x+5)-(x+5)^2 is -50 - 10x.