(4a+3)^2-(2a+1)(4a-3)

2 min read Jun 16, 2024

Simplifying the Expression: (4a + 3)² - (2a + 1)(4a - 3)

This article will guide you through the process of simplifying the algebraic expression: (4a + 3)² - (2a + 1)(4a - 3).

First, we'll expand the squared term and the product of the two binomials:

(4a + 3)²: This is a perfect square trinomial, which follows the pattern (a + b)² = a² + 2ab + b². Applying this pattern, we get: (4a + 3)² = (4a)² + 2(4a)(3) + 3² = 16a² + 24a + 9
(2a + 1)(4a - 3): This is the product of two binomials, which can be expanded using the FOIL method (First, Outer, Inner, Last). Applying this method, we get: (2a + 1)(4a - 3) = (2a)(4a) + (2a)(-3) + (1)(4a) + (1)(-3) = 8a² - 6a + 4a - 3 = 8a² - 2a - 3

Now, we have the expanded expression: 16a² + 24a + 9 - (8a² - 2a - 3)

Next, we'll distribute the negative sign to the terms inside the parentheses:

16a² + 24a + 9 - 8a² + 2a + 3

Finally, we'll combine the like terms:

(16a² - 8a²) + (24a + 2a) + (9 + 3) = 8a² + 26a + 12

Therefore, the simplified form of the expression (4a + 3)² - (2a + 1)(4a - 3) is 8a² + 26a + 12.