10a3   - 5ª +15a2  = 5ª ( 2a2 – 1 + 3a)

Let's solve the equation step by step:

Given:
\[
10a^3 - 5a + 15a^2 = 5a(2a^2 - 1 + 3a)
\]

### Step 1: Simplify the right-hand side

First, expand the right-hand side by distributing the \(5a\) over the terms inside the parentheses:

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

### Step 2: Compare both sides

Now, the equation becomes:
\[
10a^3 - 5a + 15a^2 = 10a^3 - 5a + 15a^2
\]

Since both sides of the equation are identical, the equation holds true for all values of \(a\). 

Thus, the solution is:
\[
\boxed{\text{True for all values of } a.}
\]

Would you like more details or further clarifications?

Here are 5 related questions:
1. What is an identity in algebra?
2. How do you solve quadratic equations?
3. Can all polynomial equations be simplified this way?
4. How does factoring work with higher-degree polynomials?
5. What are some techniques for solving cubic equations?

**Tip:** Always check if both sides of an equation simplify to the same expression before proceeding further!

Learn how to solve the polynomial equation 10a^3 - 5a + 15a^2 = 5a(2a^2 - 1 + 3a) step-by-step. This solution includes using the distributive property to simplify the equation, leading to a polynomial identity. Suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation