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## Algebra 2

### Course: Algebra 2>Unit 1

Lesson 6: Special products of polynomials

# Polynomial arithmetic: FAQ

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, $3{x}^{2}+2x-5$ 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 $3{x}^{2}+2x-5$ and $2{x}^{2}-3x+1$, we combine the ${x}^{2}$ terms, the $x$ terms, and the constant terms:
$\left(3{x}^{2}+2x-5\right)+\left(2{x}^{2}-3x+1\right)=5{x}^{2}-x-4$

## 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 $3x$ by $2{x}^{2}-5x+6$, we multiply $3x$ by each term of the polynomial:
$3x\left(2{x}^{2}-5x+6\right)=6{x}^{3}-15{x}^{2}+18x$

## 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 $\left(2x-3\right)\left(3x+4\right)$ using the distributive property we compute each product and combine the like $x$ terms:
$\begin{array}{rl}& 2x×3x=6{x}^{2}\\ \\ & 2x×4=8x\\ \\ & -3×3x=-9x\\ \\ & -3×4=-12\end{array}$
So $\left(2x-3\right)\left(3x+4\right)=6{x}^{2}-x-12$.

## 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:
$\left(a+b{\right)}^{2}={a}^{2}+2ab+{b}^{2}$
Another common special product is the difference of two squares:
$\left(a+b\right)\left(a-b\right)={a}^{2}-{b}^{2}$

## Want to join the conversation?

• is it just me that writes the right result on paper and type it wrong?
(61 votes)
• No, it is not.
(6 votes)
• 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!
(32 votes)
• what is the formola of (a+b)(a-b)
(4 votes)
• a^2-b^2
(15 votes)
• How to combine like terms
(6 votes)
• 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.
(6 votes)
• What is a polynomial?
(3 votes)
• 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
(6 votes)
• What would be the chances of something to happen outside 5 standard deviations?
(3 votes)
• 2X^5*71x^45
(0 votes)
• 2𝑥⁵⋅71𝑥⁴⁵
= 2⋅71⋅𝑥⁵⋅𝑥⁴⁵
= 142𝑥⁵⁺⁴⁵
= 142𝑥⁵⁰
(5 votes)
• Why is it so hard to solve these ?
(1 vote)
• It just take time to get it. Every one is different when we're learning.
(3 votes)
• how we can apply polynomial functions in real life application?
(1 vote)
• 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 :)
(3 votes)
• how does hyperbolic functions work?
(3 votes)
• 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.
(1 vote)