Q5.61 - Intermediate Algebra

Question

Multiply $(y-3)(y^2-5y+2)$ using (a) the distributive property and (b) the vertical method.

Step-by-Step Solution

Answer

$$\begin{gathered} Multiply the given binomials,we get \\ (y-3)(y^2-5y+2) \\ {y}^3-8y^2+17y-6 \end{gathered}$$

Step 1

$$\begin{gathered} Given Information: \\ Multiply (y-3)(y^2-5y+2) u\sin g \left(a\right) distrivutive property and \left(b\right) vertical method \end{gathered}$$

Step 2

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. 

Vertical addition is a method of adding where the numbers are lined up in columns according to their places value. 

Part(a) Step1. Multiply binomial using distributive property.

$$\begin{gathered} \left(a\right) \\ Distribute y\times y^2-5y\times y+2y-3\times y^2+3\times 5y-3\times 2 \\ Distribute again y^3-5y^2+2y-3y^2+15y-6 \\ Combine like terms y^3-8y^2+17y-6 \end{gathered}$$

Part(b) Step1.Multiply binomial by vertical method.

$$\begin{gathered} \left(b\right) \\ y^2 -5y+2 \\ \times (y-3) \\ Multiply y^2-5y+2 by -3 -3y^2+15y-6 \\ Multiply y^2-5y+2 by y y^3-5y^2 +2y \\ Add like terms y^3-8y^2 +17y-6 \end{gathered}$$