%5E2-4x(2x%2B3)%5E2-(2x-1)(x%2B3)(x-3).jpeg "(x+5)^2-4x(2x+3)^2-(2x-1)(x+3)(x-3)")
Simplifying the Expression (x+5)^2-4x(2x+3)^2-(2x-1)(x+3)(x-3)
This article will guide you through the process of simplifying the given algebraic expression:
(x+5)^2-4x(2x+3)^2-(2x-1)(x+3)(x-3)
Let's break it down step by step:
1. Expanding the Squares
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(x+5)^2: This is a perfect square trinomial. We can expand it using the formula (a+b)^2 = a^2 + 2ab + b^2.
So, (x+5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25
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(2x+3)^2: Similarly, we can expand this using the same formula.
(2x+3)^2 = (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9
2. Expanding the Products
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(2x-1)(x+3)(x-3): Here, we can use the difference of squares formula: (a+b)(a-b) = a^2 - b^2.
First, multiply (x+3)(x-3) = x^2 - 9. Then, multiply the result with (2x-1).
(2x-1)(x^2 - 9) = 2x^3 - 18x - x^2 + 9
3. Substituting the Expanded Forms
Now, substitute the expanded forms back into the original expression:
(x^2 + 10x + 25) - 4x(4x^2 + 12x + 9) - (2x^3 - 18x - x^2 + 9)
4. Distributing and Combining Like Terms
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Distribute -4x:
-4x(4x^2 + 12x + 9) = -16x^3 - 48x^2 - 36x
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Combine like terms:
x^2 + 10x + 25 - 16x^3 - 48x^2 - 36x - 2x^3 + 18x + x^2 - 9
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Simplify:
-18x^3 - 46x^2 - 8x + 16
Final Simplified Expression
Therefore, the simplified form of the given expression is -18x^3 - 46x^2 - 8x + 16.