(x+4)(x-2)-(x-3)^2

Jasonbradley

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Jun 16, 2024

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Expanding and Simplifying the Expression (x+4)(x-2)-(x-3)^2

This article will guide you through the process of expanding and simplifying the algebraic expression (x+4)(x-2)-(x-3)^2.

Expanding the Expressions

1. (x+4)(x-2): This is a product of two binomials. We can expand it using the FOIL method (First, Outer, Inner, Last):

   • First: x * x = x²
   • Outer: x * -2 = -2x
   • Inner: 4 * x = 4x
   • Last: 4 * -2 = -8
   • Combine the terms: x² - 2x + 4x - 8 = x² + 2x - 8

2. (x-3)^2: This is a squared binomial. We can expand it by multiplying it with itself:

   • (x-3)(x-3)
   • First: x * x = x²
   • Outer: x * -3 = -3x
   • Inner: -3 * x = -3x
   • Last: -3 * -3 = 9
   • Combine the terms: x² - 3x - 3x + 9 = x² - 6x + 9

Simplifying the Expression

Now we have: (x+4)(x-2)-(x-3)^2 = (x² + 2x - 8) - (x² - 6x + 9)

To simplify further, distribute the negative sign: x² + 2x - 8 - x² + 6x - 9

Finally, combine like terms: (x² - x²) + (2x + 6x) + (-8 - 9) = 8x - 17

Conclusion

Therefore, the simplified form of the expression (x+4)(x-2)-(x-3)^2 is 8x - 17.