(1%2B2x)%2B(1%2Bx)-(x%5E4%2Bx%5E3-5x%5E2-5).jpeg "(2-x)(1+2x)+(1+x)-(x^4+x^3-5x^2-5)")
Simplifying the Expression: (2-x)(1+2x)+(1+x)-(x^4+x^3-5x^2-5)
This article will guide you through the steps to simplify the given algebraic expression:
(2-x)(1+2x)+(1+x)-(x^4+x^3-5x^2-5)
Step 1: Expanding the Products
Let's begin by expanding the products using the distributive property:
- (2-x)(1+2x) = 2 + 4x - x - 2x²
- (1+x) = 1 + x
Step 2: Combining Like Terms
Now, let's combine the like terms from the expanded expressions:
2 + 4x - x - 2x² + 1 + x - (x^4 + x^3 - 5x^2 - 5)
This simplifies to:
-x^4 - x^3 + 3x² + 4x + 8
Step 3: Writing the Final Expression
Therefore, the simplified form of the given expression is:
-x^4 - x^3 + 3x² + 4x + 8
Conclusion
By expanding the products, combining like terms, and simplifying the expression, we have successfully simplified the given algebraic expression. This process can be applied to simplify similar expressions involving multiplications and additions of polynomials.