Question

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

Short answer

$$\begin{gathered} Multiplythegivenbinomials,weget \\ (y-3)(y^2-5y+2) \\ {y}^3-8y^2+17y-6 \end{gathered}$$

Step-by-step solution

Step 1

$$\begin{gathered} GivenInformation: \\ Multiply(y-3)(y^2-5y+2)u\sin g\left(a\right)distrivutivepropertyand\left(b\right)verticalmethod \end{gathered}$$

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.

$$\begin{gathered} \left(a\right) \\ Distributey\times y^2-5y\times y+2y-3\times y^2+3\times 5y-3\times 2 \\ Distributeagain{y}^3-5y^2+2y-3y^2+15y-6 \\ Combineliketerms{y}^3-8y^2+17y-6 \end{gathered}$$

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

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