Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials.
Include common errors to watch out for when using each of these methods.
Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.
As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication.
Describe an example of your model for the product .
Imagine that you are teaching a new student how to multiply polynomials.
Explain how multiplying polynomials is similar to multiplying integers.
Then describe the key differences between the two.
If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)?
What about multiplying a monomial by a trinomial? Two trinomials?
Write a statement about how many terms you will get when you multiply a polynomial with terms by a polynomial with terms.
Give an explanation to support your statement.
Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials.
Include common errors to watch out for when using each of these methods.
Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.
As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication.
Describe an example of your model for the product .
Imagine that you are teaching a new student how to multiply polynomials.
Explain how multiplying polynomials is similar to multiplying integers.
Then describe the key differences between the two.
If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)?
What about multiplying a monomial by a trinomial? Two trinomials?
Write a statement about how many terms you will get when you multiply a polynomial with terms by a polynomial with terms.
Give an explanation to support your statement.
Each method works differently the angles inside them is what matters.
Overall vertical is visually better, if done correctly. it forces you to “line up” all the common exponents.
The disadvantage is that it usually requires re-writing the problem, and it takes up space. most problems are presented horizontally, that becomes the issue to locate the common exponents.
In both cases the biggest issue is we forget that when subtracting “subtracting a negative is like adding a positive”
For example :
everyone misses those eventually so you have to watch out for that in both methods
We cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial because multiplying linear by a quadratic polynomial would be equal to a cubic polynomial. Algebra tiles do not model cubic functions.
Manipulating algebra tiles can help us to solve linear equations
Distribute each term of the first polynomial to every term of the second polynomial.
Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents.
But with Integers you multiply two integers with different signs
multiplying polynomials could be takes place by multiplying one term of polynomial with each term of other polynomial .the same thing should be happens with the integers where we multiply place value of one integer with place value of other integer.
When multiplying two binomials, the result before combining like terms is four terms.
When multiplying a monomial by a trinomial, the result before combining like terms is three terms.
When multiplying two trinomials, the result before combining like terms is nine terms.
The amount of terms one will get if a polynomial with m number of terms is multiplied by a polynomial with n number of terms will be the product of m and n.
If a trinomial has three terms, and a binomial has two terms, then the result before combining like terms will be six terms.
multiply each term in one polynomial by each term in the other polynomial
For Examples:
Each method works differently the angles inside them is what matters.
Overall vertical is visually better, if done correctly. it forces you to “line up” all the common exponents.
The disadvantage is that it usually requires re-writing the problem, and it takes up space. most problems are presented horizontally, that becomes the issue to locate the common exponents.
In both cases the biggest issue is we forget that when subtracting “subtracting a negative is like adding a positive”
For example :
everyone misses those eventually so you have to watch out for that in both methods
We cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial because multiplying linear by a quadratic polynomial would be equal to a cubic polynomial. Algebra tiles do not model cubic functions.
Manipulating algebra tiles can help us to solve linear equations
Distribute each term of the first polynomial to every term of the second polynomial.
Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents.
But with Integers you multiply two integers with different signs
multiplying polynomials could be takes place by multiplying one term of polynomial with each term of other polynomial .the same thing should be happens with the integers where we multiply place value of one integer with place value of other integer.
When multiplying two binomials, the result before combining like terms is four terms.
When multiplying a monomial by a trinomial, the result before combining like terms is three terms.
When multiplying two trinomials, the result before combining like terms is nine terms.
The amount of terms one will get if a polynomial with m number of terms is multiplied by a polynomial with n number of terms will be the product of m and n.
If a trinomial has three terms, and a binomial has two terms, then the result before combining like terms will be six terms.
multiply each term in one polynomial by each term in the other polynomial
For Examples:
