tell the coefficient of $$ x^2 $$in : (2x-5) (2$$ x^2 $$-3x +1)

To find the coefficient of $ x^2 $ in the expression $ (2x - 5)(2x^2 - 3x + 1) $, let's expand the expression and identify the term that contains $ x^2 $.

We'll distribute each term in $ (2x - 5) $ to every term in $ (2x^2 - 3x + 1) $:

\[
(2x - 5)(2x^2 - 3x + 1) = 2x \cdot (2x^2 - 3x + 1) - 5 \cdot (2x^2 - 3x + 1)
\]

Now, let's expand each part:

\[
2x \cdot (2x^2) = 4x^3
\]
\[
2x \cdot (-3x) = -6x^2
\]
\[
2x \cdot 1 = 2x
\]

Next, for $-5$:

\[
-5 \cdot (2x^2) = -10x^2
\]
\[
-5 \cdot (-3x) = 15x
\]
\[
-5 \cdot 1 = -5
\]

Now, combine all these results:

\[
4x^3 - 6x^2 + 2x - 10x^2 + 15x - 5
\]

Combine like terms for $ x^2 $:

\[
-6x^2 - 10x^2 = -16x^2
\]

So, the coefficient of $ x^2 $ is $\boxed{-16}$.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the coefficient of $ x^3 $ in the expansion of $ (2x - 5)(2x^2 - 3x + 1) $?
2. How do you find the constant term in the expansion of $ (2x - 5)(2x^2 - 3x + 1) $?
3. How would the coefficient of $ x^2 $ change if the expression were $ (3x - 4)(2x^2 - 3x + 1) $?
4. Can you expand $ (2x - 5)(3x^2 - x + 4) $ and find the coefficient of $ x^2 $?
5. What is the general method to expand the product of two polynomials?

**Tip:** When expanding a polynomial, focus on distributing each term carefully to avoid errors in combining like terms.

Learn how to find the coefficient of x^2 in the expansion of (2x - 5)(2x^2 - 3x + 1) with a step-by-step solution. This problem involves expanding polynomials and extracting coefficients. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation