Prove that 2(a^2)(b^2)+2(b^2)(c^2)+2(c^2)(b^2)=(a^4)(b^4)(c^4)

Let's analyze the given equation:

\[
2a^2b^2 + 2b^2c^2 + 2c^2a^2 = a^4b^4c^4
\]

We'll first check if the equation holds by simplifying each side.

### Step 1: Simplifying the left-hand side (LHS)
\[
\text{LHS} = 2a^2b^2 + 2b^2c^2 + 2c^2a^2
\]

Factor out the common factor of \( 2 \):
\[
\text{LHS} = 2(a^2b^2 + b^2c^2 + c^2a^2)
\]

This is the simplified form of the left-hand side. Now, let's check the right-hand side.

### Step 2: Right-hand side (RHS)
\[
\text{RHS} = a^4b^4c^4
\]



Prove that 2(a^2)(b^2) + 2(b^2)(c^2) + 2(c^2)(a^2) = (a^4)(b^4)(c^4)

This page walks through the step-by-step solution to prove the polynomial identity 2(a^2)(b^2) + 2(b^2)(c^2) + 2(c^2)(a^2) = (a^4)(b^4)(c^4). Learn key algebraic concepts and techniques in simplifying and factoring polynomial expressions, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation