Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Homework: Multiplying Binomials

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Homework: Multiplying Binomials

Module by: Kenny M. Felder. E-mail the author

Summary: Some homework problems on multiplying binomials.

Memorize these:

  • ( x + a ) 2 = x 2 + 2 ax + a 2 ( x + a ) 2 = x 2 + 2 ax + a 2 size 12{ \( x+a \) rSup { size 8{2} } =x rSup { size 8{2} } +2 ital "ax"+a rSup { size 8{2} } } {}
  • ( x − a ) 2 = x 2 − 2 ax + a 2 ( x − a ) 2 = x 2 − 2 ax + a 2 size 12{ \( x - a \) rSup { size 8{2} } =x rSup { size 8{2} } - 2 ital "ax"+a rSup { size 8{2} } } {}
  • x 2 − a 2 = ( x + a ) ( x − a ) x 2 − a 2 = ( x + a ) ( x − a ) size 12{x rSup { size 8{2} } - a rSup { size 8{2} } = \( x+a \) \( x - a \) } {}

Exercise 1

In the following drawing, one large square is divided into four regions. The four small regions are labeled with Roman numerals because I like to show off.

Figure 1
One large square is divided into four regions.
  • a. How long is the left side of the entire figure? _______________
  • b. How long is the bottom of the entire figure? _______________
  • c. One way to compute the area of the entire figure is to multiply these two numbers (total height times total width). Write this product down here: Area = _______________
  • d. Now: what is the area of the small region labeled I? _______________
  • e. What is the area of the small region labeled II? _______________
  • f. What is the area of the small region labeled III? _______________
  • g. What is the area of the small region labeled IV? _______________
  • h. The other way to compute the area of the entire figure is to add up these small regions. Write this sum down here: Area =_________________
  • i. Obviously, the answer to (c) and the answer to (h) have to be the same, since they are both the area of the entire figure. So write down the equation setting these two equal to each other here: ____________________________________
  • j. that look like one of our three formulae?

Exercise 2

Multiply these out “manually.”

  • a. ( x + 3 ) ( x + 4 ) ( x + 3 ) ( x + 4 ) size 12{ \( x+3 \) \( x+4 \) } {}
  • b. ( x + 3 ) ( x − 4 ) ( x + 3 ) ( x − 4 ) size 12{ \( x+3 \) \( x - 4 \) } {}
  • c. ( x − 3 ) ( x − 4 ) ( x − 3 ) ( x − 4 ) size 12{ \( x - 3 \) \( x - 4 \) } {}
  • d. ( 2x + 3 ) ( 3x + 2 ) ( 2x + 3 ) ( 3x + 2 ) size 12{ \( 2x+3 \) \( 3x+2 \) } {}
  • e. ( x − 2 ) ( x 2 + 2x + 4 ) ( x − 2 ) ( x 2 + 2x + 4 ) size 12{ \( x - 2 \) \( x rSup { size 8{2} } +2x+4 \) } {}
  • f. Check your answer to part (e) by substituting the number 3 into both my original function, and your answer. Do they come out the same?

Exercise 3

Multiply these out using the formulae above.

  • a. ( x + 3 / 2 ) 2 ( x + 3 / 2 ) 2 size 12{ \( x+ {3} slash {2} \) rSup { size 8{2} } } {}
  • b. ( x − 3 / 2 ) 2 ( x − 3 / 2 ) 2 size 12{ \( x - {3} slash {2} \) rSup { size 8{2} } } {}
  • c. ( x + 3 ) 2 ( x + 3 ) 2 size 12{ \( x+3 \) rSup { size 8{2} } } {}
  • d. ( 3 + x ) 2 ( 3 + x ) 2 size 12{ \( 3+x \) rSup { size 8{2} } } {}
  • e. ( x − 3 ) 2 ( x − 3 ) 2 size 12{ \( x - 3 \) rSup { size 8{2} } } {}
  • f. ( 3 − x ) 2 ( 3 − x ) 2 size 12{ \( 3 - x \) rSup { size 8{2} } } {}
  • g. Hey, why did (e) and (f) come out the same? ( x−3x−3 size 12{x - 3} {} isn’t the same as 3−x3−x size 12{3 - x} {}, is it?)
  • h. ( x + 1 / 2 ) ( x + 1 / 2 ) ( x + 1 / 2 ) ( x + 1 / 2 ) size 12{ \( x+ {1} slash {2} \) \( x+ {1} slash {2 \) } } {}
  • i. ( x + 1 / 2 ) ( x − 1 / 2 ) ( x + 1 / 2 ) ( x − 1 / 2 ) size 12{ \( x+ {1} slash {2} \) \( x - {1} slash {2 \) } } {}
  • j. ( 5 − 3 ) ( 5 + 3 ) ( 5 − 3 ) ( 5 + 3 ) size 12{ \( sqrt {5} - sqrt {3} \) \( sqrt {5} + sqrt {3} \) } {}
  • k. Check your answer to part (j) by running through the whole calculation on your calculator: 5−3=5−3= size 12{ sqrt {5} - sqrt {3} ={}} {}_______, 5+3=5+3= size 12{ sqrt {5} + sqrt {3} ={}} {} _______, multiply them and you get _______.

Exercise 4

Now, let’s try going backward. Rewrite the following expressions as (x+something)2(x+something)2 size 12{ \( x+"something" \) rSup { size 8{2} } } {}, or as (x−something)2(x−something)2 size 12{ \( x - "something" \) rSup { size 8{2} } } {}, or as (x+something)(x−something)(x+something)(x−something) size 12{ \( x+"something" \) \( x - "something" \) } {}. In each case, check your answer by multiplying back to see if you get the original expression.

  • a. x2−8x+16=x2−8x+16= size 12{x rSup { size 8{2} } - 8x+"16"={}} {} ____________
  • Check by multiplying back: _______________
  • b. x2−25=x2−25= size 12{x rSup { size 8{2} } - "25"={}} {} ____________
  • Check by multiplying back: _______________
  • c. x2+2x+1=x2+2x+1= size 12{x rSup { size 8{2} } +2x+1={}} {} ____________
  • Check by multiplying back: _______________
  • d. x2−20x+100=x2−20x+100= size 12{x rSup { size 8{2} } - "20"x+"100"={}} {} ____________
  • Check by multiplying back: _______________
  • e. 4x2−9=4x2−9= size 12{4x rSup { size 8{2} } - 9={}} {} ____________
  • Check by multiplying back: _______________

Exercise 5

Enough squaring: let’s go one higher, and see what (x+a)3(x+a)3 size 12{ \( x+a \) rSup { size 8{3} } } {} is!

  • a. (x+a)3(x+a)3 size 12{ \( x+a \) rSup { size 8{3} } } {} means ( (x+a)(x+a)(x+a)(x+a)(x+a)(x+a) size 12{ \( x+a \) \( x+a \) \( x+a \) } {}. You already know what (x+a)(x+a)(x+a)(x+a) size 12{ \( x+a \) \( x+a \) } {} is. So multiply that by (x+a)(x+a) size 12{ \( x+a \) } {} to find the cubed formula. (Multiply term-by-term, then collect like terms.)
  • b. Use the formula you just found to find (y+a)3(y+a)3 size 12{ \( y+a \) rSup { size 8{3} } } {}.
  • c. Use the same formula to find (y−3)3(y−3)3 size 12{ \( y - 3 \) rSup { size 8{3} } } {}.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks