Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring and Expanding Polynomials
Factoring involves breaking down a polynomial into simpler components, while expanding refers to multiplying these components to form a polynomial. Understanding how to factor and expand polynomials is crucial for simplifying expressions and solving equations in algebra.
Recommended video:
Introduction to Factoring Polynomials
Difference of Squares
The difference of squares is a specific algebraic identity that states that a² - b² can be factored into (a + b)(a - b). In the given expression, (x + 1)(x - 1) represents a difference of squares, which simplifies to x² - 1, making it easier to multiply with the remaining polynomial.
Recommended video:
Solving Quadratic Equations by Completing the Square
Polynomial Multiplication
Polynomial multiplication involves multiplying two or more polynomials together, which requires distributing each term in one polynomial to every term in the other. This process is essential for finding the product of polynomials, as seen in the final step of the given expression where the result of the first multiplication is combined with the third polynomial.
Recommended video:
Finding Zeros & Their Multiplicity