Let's expand the expression \((2x−1)(x+9)\) using the distributive property (also known as the FOIL method for binomials).

\[
(2x - 1)(x + 9) = 2x(x + 9) - 1(x + 9)
\]

Now distribute each term:

\[
= 2x \cdot x + 2x \cdot 9 - 1 \cdot x - 1 \cdot 9
\]

Simplifying each multiplication:

\[
= 2x^2 + 18x - x - 9
\]

Now combine like terms:

\[
= 2x^2 + 17x - 9
\]

So, the expanded form of \((2x−1)(x+9)\) is:

\[
2x^2 + 17x - 9
\]

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How do you factor quadratic expressions like \(2x^2 + 17x - 9\)?
2. What is the solution to the equation \(2x^2 + 17x - 9 = 0\)?
3. How would you apply the distributive property to a trinomial?
4. Can you explain how to simplify like terms in polynomial expressions?
5. How do you identify the coefficients in a quadratic expression?

**Tip:** Always organize your terms by powers of \(x\) to ensure clarity when simplifying expressions.

Learn how to expand the binomial expression (2x−1)(x+9) using the distributive property. This step-by-step solution covers key algebraic concepts such as polynomial expansion, the FOIL method, and combining like terms. Suitable for students in Grades 7-9.

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