(x-6).jpeg "(2x+3)(x-6)")
Expanding and Simplifying the Expression (2x + 3)(x - 6)
This article will guide you through the process of expanding and simplifying the expression (2x + 3)(x - 6).
Understanding the Process
The expression (2x + 3)(x - 6) represents the product of two binomials. To expand this expression, we will use the distributive property or the FOIL method.
Distributive Property:
- Distribute each term in the first binomial to each term in the second binomial.
- This means multiplying 2x with both x and -6, then multiplying 3 with both x and -6.
FOIL Method:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's use the distributive property:
(2x + 3)(x - 6) = 2x(x - 6) + 3(x - 6)
Now, distribute:
= 2x * x + 2x * -6 + 3 * x + 3 * -6
Simplify:
= 2x² - 12x + 3x - 18
Simplifying the Expression
Combine like terms:
= 2x² - 9x - 18
Final Result
Therefore, the expanded and simplified form of the expression (2x + 3)(x - 6) is 2x² - 9x - 18.
This expression represents a quadratic polynomial with a leading coefficient of 2, a linear coefficient of -9, and a constant term of -18.