Factoring Difference of Two Squares
Recommended Books on Amazon (affiliate links) | ||
---|---|---|
![]() |
![]() |
![]() |
A special case that you will definitely come across in calculus is the difference of two squares.
The difference of two squares equation is pretty easy.
\( a^2 - b^2 = (a+b)(a-b) \) |
---|
Note - There is no equation to factor the sum to two squared terms, i.e. \( a^2 + b^2 \) where you end up with real terms. Since calculus uses mostly real numbers, you won't need to factor the sum of two squares until you start working with complex numbers.
Okay, let's use the formula for the difference of two squares on some practice problems.
Unless otherwise instructed, factor these polynomials, giving your answers in exact form.
\( x^4 - 81 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( x^4 - 81 \)
Solution
video by Freshmen Math Doctor |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
\( 36x^2 - 49y^2 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 36x^2 - 49y^2 \)
Solution
video by Freshmen Math Doctor |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
\( 64x^2 - 81 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 64x^2 - 81 \)
Solution
video by Freshmen Math Doctor |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
\( x^2 - 144 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( x^2 - 144 \)
Solution
video by Freshmen Math Doctor |
---|
Log in to rate this practice problem and to see it's current rating. |
---|
\( 16x^2 - 81y^4 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 16x^2 - 81y^4 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( 9x^2 - 49 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 9x^2 - 49 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( 36y^4 - 100 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 36y^4 - 100 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( 16x^2 - 25y^2 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 16x^2 - 25y^2 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( 64x^2 - 81y^2 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( 64x^2 - 81y^2 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( (x-3)^2 - 4 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( (x-3)^2 - 4 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( (x+7)^2 - 25 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( (x+7)^2 - 25 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
\( (x+2)^2 - 25 \)
Problem Statement
Unless otherwise instructed, factor the polynomial \( (x+2)^2 - 25 \)
Solution
Log in to rate this practice problem and to see it's current rating. |
---|
Really UNDERSTAND Precalculus
Log in to rate this page and to see it's current rating.
To bookmark this page and practice problems, log in to your account or set up a free account.
Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.
| |
I recently started a Patreon account to help defray the expenses associated with this site. To keep this site free, please consider supporting me. |
---|
Support 17Calculus on Patreon |
|
---|