https://r2.erweima.ai/mathbot/image/1726315083278ppm0bcqg.jpg

The expression shown in the image is:

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

We can expand this expression by using the distributive property (also known as FOIL method in this case):

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

Let's distribute and simplify:

1. Distribute \( x \):
\[
x(2x^2 - 3x + 5) = 2x^3 - 3x^2 + 5x
\]

2. Distribute \( 1 \):
\[
1(2x^2 - 3x + 5) = 2x^2 - 3x + 5
\]

Now, combine the like terms:
\[
2x^3 - 3x^2 + 5x + 2x^2 - 3x + 5 = 2x^3 - x^2 + 2x + 5
\]

So, the expanded form of the expression is:
\[
2x^3 - x^2 + 2x + 5
\]

Would you like further clarification or a breakdown of any specific step?

### Related Questions:
1. How can I expand binomials using the FOIL method?
2. What is the distributive property, and how does it apply to polynomials?
3. Can we factor this expanded polynomial back into its original form?
4. How can I apply this method to more complicated expressions?
5. What are the common mistakes when expanding binomials and polynomials?

### Tip:
When expanding polynomials, always carefully group and simplify like terms to avoid errors.

Explore the polynomial expansion of (x + 1)(2x^2 - 3x + 5) with step-by-step details. Learn how to apply the distributive property to expand and simplify polynomials. Suitable for students in Grades 8-10.

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