ight) + 5 $. Simplify: $ g(u) = (u - 3)^2 + 6(u - 3) + 5 = u^2 - 6u + 9 + 6u - 18 + 5 = u^2 - 4 $. Thus, $ g(x^2 - 1) = (x^2 - 1)^2 - 4 = x^4 - 2x^2 + 1 - 4 = x^4 - 2x^2 - 3 $. Final answer: $oxed{x^4 - 2x^2 - 3}$

Mon, 20 Apr 2026 08:07:58 +0000

How to Simplify Quadratic Functions: Simplifying $ g(u) $ and Finding $ g(x^2 - 1) $ Understanding how to simplify quadratic functions is essential for solving equations and working with algebraic expressions efficiently. In this article, we’ll walk through simplifying a quadratic function $ g(u) $, then use it to compute $ g(x^2 - 1) $, demonstrating step-by-step simplification. This method can help simplify complex expressions in algebra and calculus. --- ### Step 1: Simplify the Quadratic Function $ g(u) $