(x%5E3-3x%5E2-x%2B1).jpeg "(-2x)(x^3-3x^2-x+1)")
Factorization of Algebraic Expressions: Evaluating (-2x)(x^3-3x^2-x+1)
In algebra, factorization is a crucial concept used to simplify complex expressions and equations. One such expression is (-2x)(x^3-3x^2-x+1), which we will evaluate and simplify in this article.
The Expression
The given expression is:
(-2x)(x^3-3x^2-x+1)
To simplify this expression, we need to follow the order of operations (PEMDAS) and multiply the two binomials.
Multiplying the Binomials
To multiply (-2x) with (x^3-3x^2-x+1), we need to follow the distributive property of multiplication over subtraction. The result is:
-2x(x^3) + 6x^3 - 2x(x) + 2x -2x^4 + 6x^3 + 2x^2 - 2x + 2x -2x^4 + 6x^3 + 2x^2
Simplifying the Expression
By combining like terms, we get:
-2x^4 + 6x^3 + 2x^2
Thus, the simplified expression is -2x^4 + 6x^3 + 2x^2.
Conclusion
In this article, we evaluated and simplified the algebraic expression (-2x)(x^3-3x^2-x+1) by applying the distributive property of multiplication over subtraction and combining like terms. The final simplified expression is -2x^4 + 6x^3 + 2x^2.
