Calculating Rectangle Area: Polynomial Multiplication Example
Solve for the area of a rectangle using polynomial multiplication. Understand how to multiply monomials and binomials, apply the distributive property, and find the product. Step-by-step illustrations provided.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
SOLVE The length of a rectangle is represented by the polynomial 2x2+ 4x + 5. The width of the rectangle is represented by the monomial 3x. What is the area of the rectangle? S Study the Problem Underline the question. This problem is asking me to find the area of the rectangle.
Multiply a Monomial by a Binomial Let s start our lesson with some simple multiplication. Using our algebra tiles, let s multiply 2 3. 2 3 means we have 2 groups with 3 items in each group. 2 3 = 6 We will use the same method to multiply polynomials. Represent the first factor vertically and the second factor horizontally. The area created by the factors is the product!
Multiply a Monomial by a Binomial Problem 1: x(x+3) The first factor will be represented vertically with a yellow x tile. The second factor will be represented horizontally with a yellow x tile and 3 small yellow squares. We can find the product of this monomial and polynomial by finding the area that they create with a length of x and a width of x + 3.
Multiply a Monomial by a Binomial Problem 1: x(x+3) x times x gives us a product of x2 x times 3 gives us a product of 3x The product is 1 yellow x2 tile and 3 yellow x tiles, or x2 + 3x.
Multiply a Monomial by a Binomial Problem 2: (x+3)x The first factor will be represented vertically with a yellow x tile and 3 small yellow squares. The second factor will be represented horizontally with a yellow x tile. We can find the product of this monomial and polynomial by finding the area that they create with a length of x + 3 and a width of x.
Multiply a Monomial by a Binomial Problem 2: (x+3)x x times x gives us a product of x2 3 times x gives us a product of 3x The product is 1 yellow x2 tile and 3 yellow x tiles, or x2 + 3x.
Multiply Polynomials without Tiles Problem 1: 2x (4x + 5) To multiply without tiles, we can draw arrows from the monomial to each term of the binomial displaying the distributive property. = 8x2+ 10x 2x (4x + 5) 2x 4x = 8x2 2x 5= 10x
Multiply Polynomials without Tiles Problem 3: 3x (x2 x 1) Without using tiles, draw arrows to multiply the monomial by the polynomial. 3x (x2 x 1) = 9x3 3x2 3x 3x x2= 9x3 3x x= 3x2 3x 1= 3x
Multiply Polynomials without Tiles Problem 5: 2x (3x + 1) To multiply without tiles, we can draw arrows from the monomial to each term of the binomial displaying the distributive property. 2x (3x + 1) = 6x2 2x 2x 3x = 6x2 2x 1= 2x
Multiply Polynomials without Tiles Problem 5: 2x (3x2 2x) To multiply without tiles, we can draw arrows from the monomial to each term of the binomial displaying the distributive property. 2x (3x2 2x) = 6x3 4x2 2x 3x2= 6x3 2x 2x= 4x2
Multiply Polynomials without Tiles Problem 9: 2x (3x2+ 5x 1) Without using tiles, draw arrows to multiply the monomial by the polynomial. 2x (3x2+5x 1) = 6x3 10x2 + 2x 2x 3x2= 6x3 2x 5x= 10x2 2x 1= 2x
SOLVE The length of a rectangle is represented by the polynomial 2x2 + 4x + 5. The width of the rectangle is represented by the monomial 3x. What is the area of the rectangle? S Study the Problem Underline the question. This problem is asking me to find the area of the rectangle.
SOLVE The length of a rectangle is represented by the polynomial 2x2 + 4x + 5. The width of the rectangle is represented by the monomial 3x. What is the area of the rectangle? O Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. Length: 2x2 + 4x + 5 Width: 3x
L Line Up a Plan Choose an operation or operations. Multiplication Write in words what your plan of action will be. Multiply the length by the width.
V Verify Your Plan with Action Estimate your answer. A polynomial Carry out your plan. (2x2 + 4x + 5)(3x) = 6x3 + 12x2 + 15x
E Examine Your Results Does your answer make sense? (compare your answer to question.) Yes, because we are looking for the area of the rectangle. Is your answer reasonable? (compare your answer to the estimate.) Yes, because our answer is a polynomial.
Is your answer accurate? (check your work.) Yes. Write your answer in a complete sentence. The area of the rectangle is 6x3 + 12x2 + 15x units2.
