Let's solve the expression \( 5x^2(2x^2 + 13x - 5) \) by distributing \( 5x^2 \) to each term inside the parentheses.

### Step 1: Distribute \( 5x^2 \)
Multiply \( 5x^2 \) by each term inside the parentheses:

\[
5x^2 \cdot 2x^2 = 10x^4
\]
\[
5x^2 \cdot 13x = 65x^3
\]
\[
5x^2 \cdot (-5) = -25x^2
\]

### Step 2: Write the final expression
After distributing, the expression becomes:

\[
10x^4 + 65x^3 - 25x^2
\]

So, the simplified expression is \( 10x^4 + 65x^3 - 25x^2 \).

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Would you like more details on any specific step or have any questions?

Here are 5 related questions you can explore:

1. How do you factor a cubic or quartic polynomial like \( 10x^4 + 65x^3 - 25x^2 \)?
2. What is the difference between factoring and expanding polynomials?
3. How do you solve polynomial equations after expanding them?
4. Can polynomials have negative exponents or fractions?
5. What are some common mistakes when distributing terms in algebraic expressions?

**Tip:** When distributing terms, always multiply both the coefficients and the variables, paying attention to their exponents!

Learn how to expand the polynomial 5x^2(2x^2 + 13x − 5) step-by-step using the distributive property. This guide covers key algebraic concepts, including polynomial expansion and the distributive law. Suitable for students in Grades 9-12.

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