Multiplying Polynomials and Simplifying Expressions

Consider the expression -3(y - 5)2 - 9 + 7y. Which statements are true about the process and simplified product? Check all that apply.

There are 3 terms in the simplified product. The final simplified product is -3y2 + 37y - 84.

Which polynomial expression represents a sum of cubes?

(6 + s)(s^2 - 6s + 36)

What is the value Shana should have written?

-2xy

Shana used a table to multiply the polynomials 2x + y and 5x - y + 3. Her work is shown below. Muriel told Shana that one of the products in the table was incorrect. Which value in the table is incorrect?

-2y

Find a simplified expression to represent the area of the triangle. The area formula for a triangle is bh, where b is the base and h is the height. The expression that represents the area of this triangle is...

4x^2 + 22x - 12cm^2

What is the product of 3a + 5 and 2a^2 + 4a - 2?

6a^3 + 22a^2 + 14a - 10

A, B, and C are polynomials, where: A = 3x - 4 B = x + 7 C = x2 + 2 What is A2 - (B + C) in simplest form?

8x^2 - 25x + 7

Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 - 2x + 3). Explain how you arrived at your answer.

To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x^2 by x^2, you add the exponents to get x^4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x^4 term, an x^3 term, an x^2 term, an x term, and a constant term.

What is the product of 2x + y and 5x - y + 3?

10x^2 + 3xy + 6x - y^2 + 3y

What is the product of 6x - y and 2x - y + 2?

12x^2 - 8xy + 12x + y^2 - 2y