reduce this 3·5·(2x^2  +x)^4·(2·2x+1)

Let's simplify the given expression step by step:

Given expression:
\[
3 \cdot 5 \cdot (2x^2 + x)^4 \cdot (2 \cdot 2x + 1)
\]

1. **Multiply the constants**: \(3 \cdot 5 = 15\).
   \[
   15 \cdot (2x^2 + x)^4 \cdot (4x + 1)
   \]

Now, the simplified expression is:
\[
15 \cdot (2x^2 + x)^4 \cdot (4x + 1)
\]

This is the fully reduced form.

Would you like to expand it further or keep it in this factored form? 

Here are some related questions for practice:

1. How would you expand \( (2x^2 + x)^4 \)?
2. Can you factor \( 4x + 1 \) further?
3. What happens if \( x = 0 \) in the expression?
4. How would the expression change if we differentiated it with respect to \( x \)?
5. What is the value of the expression when \( x = 1 \)?

**Tip**: Factored form is often preferable in expressions involving large powers because it’s more compact and easier to work with for further operations, like differentiation.

reduce this 3·5·(2x^2 + x)^4·(2·2x + 1)

Learn how to simplify and factor the algebraic expression 3·5·(2x^2 + x)^4·(4x + 1) with step-by-step instructions. This problem covers key algebraic concepts like exponentiation, factoring, and the distributive property. Suitable for students in Grades 10-12.

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