%5E2-3(x-2)(x%2B4)-7.jpeg "(2x-3)^2-3(x-2)(x+4)-7")
Simplifying the Expression: (2x - 3)^2 - 3(x - 2)(x + 4) - 7
This article will guide you through simplifying the algebraic expression: (2x - 3)^2 - 3(x - 2)(x + 4) - 7.
Step 1: Expanding the Squares and Products
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(2x - 3)^2: This is a square of a binomial. We can expand it using the formula: (a - b)^2 = a^2 - 2ab + b^2.
- Applying this, we get: (2x - 3)^2 = (2x)^2 - 2(2x)(3) + (-3)^2 = 4x^2 - 12x + 9.
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3(x - 2)(x + 4): This is a product of three terms. We can expand it step by step:
- First, expand the product (x - 2)(x + 4) using the FOIL method (First, Outer, Inner, Last): (x - 2)(x + 4) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8.
- Then, multiply the result by 3: 3(x^2 + 2x - 8) = 3x^2 + 6x - 24.
Step 2: Combining the Terms
Now we have: 4x^2 - 12x + 9 - (3x^2 + 6x - 24) - 7. Remember to distribute the negative sign:
4x^2 - 12x + 9 - 3x^2 - 6x + 24 - 7
Step 3: Simplifying the Expression
Finally, combine like terms:
(4x^2 - 3x^2) + (-12x - 6x) + (9 + 24 - 7) = x^2 - 18x + 26
Conclusion
Therefore, the simplified form of the expression (2x - 3)^2 - 3(x - 2)(x + 4) - 7 is x^2 - 18x + 26.