To simplify the expression \( 7(2x - 1)(3x + 2) \), we need to apply the distributive property (also known as FOIL for binomials) and simplify:

1. First, distribute \( (2x - 1) \) and \( (3x + 2) \):
\[
(2x - 1)(3x + 2) = 2x(3x) + 2x(2) - 1(3x) - 1(2)
\]
\[
= 6x^2 + 4x - 3x - 2
\]
\[
= 6x^2 + x - 2
\]

2. Now, multiply the entire result by 7:
\[
7(6x^2 + x - 2) = 42x^2 + 7x - 14
\]

Thus, the simplified expression is:
\[
42x^2 + 7x - 14
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you expand expressions with more than two binomials?
2. What happens when the coefficients in binomials are negative?
3. Can you factor the final expression \( 42x^2 + 7x - 14 \)?
4. How do you solve quadratic equations like \( 42x^2 + 7x - 14 = 0 \)?
5. What are the differences between simplifying and solving an equation?

**Tip:** Always check if your final expression can be factored or simplified further!

Learn how to simplify the expression 7(2x -1)(3x +2) step-by-step using the distributive property and multiplication of binomials. This detailed solution explains the key algebraic concepts, making it ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation