(x-2)-in-standard-form.jpeg "(x+3)(x-2) In Standard Form")
Expanding and Simplifying (x+3)(x-2)
In mathematics, we often encounter expressions in factored form, like (x+3)(x-2). To understand the behavior of this expression and use it effectively in equations or other calculations, we need to expand it into standard form.
Expanding the Expression
To expand the expression, we use the distributive property, also known as the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -2 = -2x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * -2 = -6
This gives us: x² - 2x + 3x - 6
Simplifying the Expression
Finally, we combine the like terms:
x² + x - 6
Conclusion
Therefore, the standard form of the expression (x+3)(x-2) is x² + x - 6. This simplified form is easier to work with in many mathematical contexts.