Question

Express the product of (1/2y^2 - 1/3y) and (12y + 3/5) as a trinomial

Answer 1

The product of the binomials (1/2y^2 - 1/3y) and (12y + 3/5) is obtained by multiplying each term of one binomial by each term of the other. After applying the distributive property (FOIL) and combining like terms, the trinomial expression is 6y^3 - (37/10)y^2 - 1/5y.

Step-by-step explanation:

The product of the binomials (1/2y2 - 1/3y) and (12y + 3/5) requires us to use the distributive property, also known as the FOIL method, to multiply each term of the first binomial by each term of the second binomial. We proceed with the multiplication as follows:

• Multiply (1/2y2) by (12y) to get 6y3.
• Multiply (1/2y2) by (3/5) to get 3/10y2.
• Multiply (-1/3y) by (12y) to get -4y2.
• Multiply (-1/3y) by (3/5) to get -1/5y.

Next, we combine like terms to express the result as a trinomial:

6y3 + (3/10y2 - 4y2) - 1/5y

After combining the y2 terms:

6y3 - (37/10)y2 - 1/5y

This is the final expression of the product as a trinomial.

Answer 2

1/2y^2*12y + 1/2y^2*3/5 -1/3y*12y +1/3y*3/5
6y^3 + 3/10y^2 - 4y^2 + 1/5y
6y^3 -37/10y^2 + 1/5y