(x%2B2)-in-standard-form.jpeg "(x+6)(x+2) In Standard Form")
Expanding and Simplifying (x+6)(x+2)
This article will guide you through the process of expanding and simplifying the expression (x+6)(x+2) into standard form.
Understanding Standard Form
Standard form for a quadratic expression is ax² + bx + c, where a, b, and c are constants.
Expanding the Expression
To expand the expression, we use the distributive property (also known as FOIL):
- 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: 6 * x = 6x
- Last: Multiply the last terms of each binomial: 6 * 2 = 12
This gives us the expanded expression: x² + 2x + 6x + 12
Simplifying the Expression
Now, we combine the like terms:
x² + (2x + 6x) + 12
This simplifies to:
x² + 8x + 12
Conclusion
Therefore, the standard form of the expression (x+6)(x+2) is x² + 8x + 12.