How to combine like terms

Just learning this but it's basically adding or subtracting terms that have the same variable and degree/exponent. For example adding 3x^2 with 4x^2 is 7x^2. an example with subtraction is 6x^3 with -4x^3 is 2x^3. Some examples of not combining like terms is 9x^3 and 4x^4 due to them having different degrees/exponents. 9x^3 and 10y^3 would not work due to different variables.

Why is it so hard to solve these ?

It just take time to get it. Every one is different when we're learning.

how we can apply polynomial functions in real life application?

Glad you asked! Firstly, tests such as the ACT or SAT may test you on these concepts, as well as concepts that are built off of polynomial functions. By learning about polynomial functions, you can make sure that you get those questions right on your ACT/SAT, which can help you secure a good college. Even after high school and college, many jobs still require knowledge about polynomial functions. Software engineers, data analysts, and astronomers are all highly desirable positions, and they all require you to know how to utilize polynomial functions, as well as concepts built off of them. Hope this helps you :)

2𝑥⁵⋅71𝑥⁴⁵ = 2⋅71⋅𝑥⁵⋅𝑥⁴⁵ = 142𝑥⁵⁺⁴⁵ = 142𝑥⁵⁰

Main content

Algebra 2

Course: Algebra 2 > Unit 1

Lesson 6: Special products of polynomials

Polynomial arithmetic: FAQ

Google Classroom

Frequently asked questions about polynomial arithmetic

What is a polynomial?

A polynomial is a type of mathematical expression made up of one or more terms. Each term consists of a variable (usually

x

) raised to a non-negative integer exponent, and multiplied by a coefficient. For example,

3 x^{2} + 2 x - 5

is a polynomial.

Why do we need to know how to add, subtract, and multiply polynomials?

Polynomial arithmetic is important for solving a variety of problems in mathematics, physics, engineering, and more. For example, knowing how to multiply polynomials can help us factor them, which in turn can be useful for solving polynomial equations.

How do we add or subtract two polynomials?

We can add or subtract two polynomials by combining like terms. For example, to add

3 x^{2} + 2 x - 5

and

2 x^{2} - 3 x + 1

, we combine the

x^{2}

terms, the

x

terms, and the constant terms:

(3 x^{2} + 2 x - 5) + (2 x^{2} - 3 x + 1) = 5 x^{2} - x - 4

How do we multiply a monomial by a polynomial?

To multiply a monomial (a polynomial with just one term) by a polynomial, we use the distributive property. For example, to multiply

3 x

2 x^{2} - 5 x + 6

, we multiply

3 x

by each term of the polynomial:

3 x (2 x^{2} - 5 x + 6) = 6 x^{3} - 15 x^{2} + 18 x

How do we multiply two binomials?

We can use the distributive property or an area model to multiply two binomials (polynomials with two terms). For example, to multiply

(2 x - 3) (3 x + 4)

using the distributive property we compute each product and combine the like

x

terms:

\begin{aligned} 2 x \times 3 x = 6 x^{2} \\ 2 x \times 4 = 8 x \\ - 3 \times 3 x = - 9 x \\ - 3 \times 4 = - 12 \end{aligned}

(2 x - 3) (3 x + 4) = 6 x^{2} - x - 12

What are special products of polynomials?

There are certain polynomial products that occur frequently in mathematics, and it's helpful to recognize them.

For example, the square of a binomial is:

(a + b)^{2} = a^{2} + 2 a b + b^{2}

Another common special product is the difference of two squares:

(a + b) (a - b) = a^{2} - b^{2}

Want to join the conversation?

Sort by:

sarra
Posted 4 months ago. Direct link to sarra's post “is it just me that writes...”
is it just me that writes the right result on paper and type it wrong?
Button navigates to signup pageComment on sarra's post “is it just me that writes...”
(61 votes)
Answer
- WolfyNightshade
  Posted 2 months ago. Direct link to WolfyNightshade's post “No, it is not.”
  No, it is not.
  Button navigates to signup page
  (6 votes)
Rosie
Posted 3 months ago. Direct link to Rosie's post “I hope that all you beaut...”
I hope that all you beautiful people are having a wonderful day! If you get stressed, remember to breath and try again! I hope everyone has a blessed day!
Button navigates to signup pageButton navigates to signup page
(32 votes)
Answer
qaimalishigri7788
Posted 5 months ago. Direct link to qaimalishigri7788's post “what is the formola of (a...”
what is the formola of (a+b)(a-b)
Button navigates to signup pageComment on qaimalishigri7788's post “what is the formola of (a...”
(4 votes)
Answer
- Mack
  Posted 5 months ago. Direct link to Mack's post “a^2-b^2”
  a^2-b^2
  Button navigates to signup page
  (15 votes)
74322ag
Posted a year ago. Direct link to 74322ag's post “How to combine like terms”
How to combine like terms
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- samloldoge3
  Posted a year ago. Direct link to samloldoge3's post “Just learning this but it...”
  Just learning this but it's basically adding or subtracting terms that have the same variable and degree/exponent. For example adding 3x^2 with 4x^2 is 7x^2. an example with subtraction is 6x^3 with -4x^3 is 2x^3. Some examples of not combining like terms is 9x^3 and 4x^4 due to them having different degrees/exponents. 9x^3 and 10y^3 would not work due to different variables.
  Button navigates to signup page
  (6 votes)
24dmerida
Posted a year ago. Direct link to 24dmerida's post “What is a polynomial?”
What is a polynomial?
Button navigates to signup pageComment on 24dmerida's post “What is a polynomial?”
(3 votes)
Answer
- longbow737
  Posted a year ago. Direct link to longbow737's post “A polynomial is a group o...”
  A polynomial is a group of numbers with more than one term. 'Poly' meaning many, and 'nomial' referring to the numbers. A binomial is a polynomial, it is just describing that there are two terms, and a trinomial is with 3 terms. Hope that helps
  Comment on longbow737's post “A polynomial is a group o...”
  (6 votes)
yubra000
Posted 4 months ago. Direct link to yubra000's post “What would be the chances...”
What would be the chances of something to happen outside 5 standard deviations?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
MuhammadYasin
Posted 6 months ago. Direct link to MuhammadYasin's post “2X^5*71x^45”
2X^5*71x^45
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- Jerry Nilsson
  Posted 6 months ago. Direct link to Jerry Nilsson's post “2𝑥⁵⋅71𝑥⁴⁵ = 2⋅71⋅𝑥⁵⋅𝑥...”
  2𝑥⁵⋅71𝑥⁴⁵
  = 2⋅71⋅𝑥⁵⋅𝑥⁴⁵
  = 142𝑥⁵⁺⁴⁵
  = 142𝑥⁵⁰
  Button navigates to signup page
  (5 votes)
kevin.shibu
Posted 2 months ago. Direct link to kevin.shibu's post “Why is it so hard to solv...”
Why is it so hard to solve these ?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Strawberry20
  Posted 2 months ago. Direct link to Strawberry20's post “It just take time to get ...”
  It just take time to get it. Every one is different when we're learning.
  Button navigates to signup page
  (3 votes)
shegaye04
Posted 2 months ago. Direct link to shegaye04's post “how we can apply polynomi...”
how we can apply polynomial functions in real life application?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- (YC) DoD
  Posted a month ago. Direct link to (YC) DoD's post “Glad you asked! Firstly, ...”
  Glad you asked! Firstly, tests such as the ACT or SAT may test you on these concepts, as well as concepts that are built off of polynomial functions. By learning about polynomial functions, you can make sure that you get those questions right on your ACT/SAT, which can help you secure a good college.
  
  Even after high school and college, many jobs still require knowledge about polynomial functions. Software engineers, data analysts, and astronomers are all highly desirable positions, and they all require you to know how to utilize polynomial functions, as well as concepts built off of them.
  
  Hope this helps you :)
  Button navigates to signup page
  (3 votes)
Zidong Qiu
Posted a year ago. Direct link to Zidong Qiu's post “how does hyperbolic funct...”
how does hyperbolic functions work?
Button navigates to signup pageComment on Zidong Qiu's post “how does hyperbolic funct...”
(3 votes)
Answer
- jl1321882
  Posted 10 months ago. Direct link to jl1321882's post “In mathematics, hyperboli...”
  In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.
  Button navigates to signup page
  (1 vote)