2-a2(a-2)(a%2B2)%2B2a(7%2B3a2).jpeg "(3a-a2)2-a2(a-2)(a+2)+2a(7+3a2)")
Simplifying the Expression (3a - a²)² - a²(a - 2)(a + 2) + 2a(7 + 3a²)
This article will guide you through simplifying the algebraic expression: (3a - a²)² - a²(a - 2)(a + 2) + 2a(7 + 3a²). We will break down the steps to achieve a simplified form.
Step 1: Expanding the Squares and Products
Let's start by expanding the squares and products in the expression:
- (3a - a²)²: This is a perfect square trinomial, expanding to (3a - a²)(3a - a²) = 9a² - 6a³ + a⁴
- a²(a - 2)(a + 2): This is a difference of squares, simplifying to a²(a² - 4) = a⁴ - 4a²
- 2a(7 + 3a²): This expands to 14a + 6a³
Step 2: Combining Like Terms
Now, let's rewrite the expression with the expanded terms and combine the like terms:
(9a² - 6a³ + a⁴) - (a⁴ - 4a²) + (14a + 6a³)
This simplifies to:
9a² - 6a³ + a⁴ - a⁴ + 4a² + 14a + 6a³
Step 3: Final Simplification
After combining like terms, we get:
13a² + 14a
Therefore, the simplified form of the expression (3a - a²)² - a²(a - 2)(a + 2) + 2a(7 + 3a²) is 13a² + 14a.