Question

Expand the expression to a polynomial in standard form: (2x+1)(x
2+4x-5

Answer 1

To expand the expression (2x+1)(x^2+4x-5), we use the distributive property to multiply each term in the first binomial by each term in the second polynomial, combine like terms, and express it in standard form as 2x^3+9x^2-6x-5.

Step-by-step explanation:

The student is asking to expand and express as a polynomial in standard form the given expression (2x+1)(x^2+4x-5).

We start by using the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second polynomial:

1. Multiply 2x by each term in (x^2+4x-5), which gives 2x^3+8x^2-10x.
2. Then, multiply 1 by each term in (x^2+4x-5), which results in x^2+4x-5.
3. Add the results together to get the expanded form: 2x^3+8x^2-10x+x^2+4x-5.
4. Finally, combine like terms to write the polynomial in standard form: 2x^3+9x^2-6x-5.

The expanded polynomial in standard form is 2x^3+9x^2-6x-5.