https://file.aiquickdraw.com/mathbot/file/172667345389737d7yktu.jpg

The problem provided is to express the product of two binomials as a trinomial. Let's solve the expression:

\[
(2x - 3)(3x - 7)
\]

We can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand this.

### Step-by-step expansion:

1. **First**: Multiply the first terms of each binomial:
   \[
   2x \times 3x = 6x^2
   \]

2. **Outer**: Multiply the outer terms:
   \[
   2x \times -7 = -14x
   \]

3. **Inner**: Multiply the inner terms:
   \[
   -3 \times 3x = -9x
   \]

4. **Last**: Multiply the last terms:
   \[
   -3 \times -7 = 21
   \]

Now, combine all the terms:

\[
6x^2 - 14x - 9x + 21
\]

Combine the like terms \(-14x\) and \(-9x\):

\[
6x^2 - 23x + 21
\]

Thus, the expression in trinomial form is:

\[
6x^2 - 23x + 21
\]

Would you like further details on this or have any questions?

Here are five related questions:
1. How would you factorize the trinomial \(6x^2 - 23x + 21\)?
2. Can this method be applied to more complex binomials, such as \((3x^2 - 4)(2x + 5)\)?
3. How does the distributive property extend to multiplying polynomials with more than two terms?
4. What happens if one of the binomials contains a fraction, such as \((2x - \frac{1}{2})(3x + 4)\)?
5. What is the relationship between the coefficients of the expanded trinomial and the original binomials?

**Tip:** Always check that like terms are combined properly when expanding binomials.

Learn how to express the product of two binomials, (2x - 3)(3x - 7), as a trinomial. This problem demonstrates key algebraic techniques like the distributive property and combining like terms. Suitable 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