Q5.54 - Intermediate Algebra

Question

Multiply : $$\begin{gathered} \left(a\right) (5x+9)(4x+3) \\ \left(b\right) (5y+2)(6y-3) \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} Multiply the given binomials ,we get \\ \left(a\right) (5x+9)(4x+3) \\ 20x^2+51x+27 \\ \left(b\right) (5y+2)(6y-3) \\ 30y^2-3y-6 \end{gathered}$$

Step 1

Given information:

$$\begin{gathered} \left(a\right) (5x+9)(4x+3) \\ \left(b\right) (5y+2)(6y-3) \end{gathered}$$

Step 2

Distributive Property:

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

Step 3 Part(a) Step 1. multiply the given binomials

$$\begin{gathered} \left(a\right)(5x+9)(4x+3) \\ Distribute: 5x(4x+3)+9(4x+3) \\ Distribute again: 20x^2+15x+36x+27 \\ Combine like terms: 20x^2+51x+27 \end{gathered}$$

Step 4 Part(b) Step 1.Multiply the binomials

$$\begin{gathered} \left(b\right)(5y+2)(6y-3) \\ Distribute:5y(6y-3)+2(6y-3) \\ Distribute again: 30y^2-15y+12y-6 \\ Combine like terms: 30y^2-3y-6 \end{gathered}$$