answersLogoWhite

0


Best Answer

First, memorize this equation: (a-b)(a-b), which, factored out will be: a2-2ab+b2 or, if your bionomial looks like this... (a+b)(a+b), leave everything positive and you'll get a2+2ab+b2 If you don't know how to get to those aswers, use the FOIL method, which stands for Firsts, Outer, Inner, Last! For this example use (a+b)(a+b) First - multiply the first variable in the first paranthesis with the first in the second parenthesis. (a+b)(a+b) a x a = a2 Outer - multiply the outer 2 variables. Use the first variable of the first parenthesis and the last of the second parenthesis. (a+b)(a+b) a x b = ab Inner - multiply the inner variables. Use the second variable of the first parenthisis and the first variable of the second parenthesis. (a+b)(a+b) b x a = ba or also written as ab Last - multiply the last variables. (a+b)(a+b) b x b = b2 Now when you add all that together, you have a2+ab+ba+b2 which, in its smallest version is a2+2ab+b2 A generalized way of doing this is to use the formula for the binomial coefficient: C(n,k) = n!/(k!(n-k)!). This formula is actually a nice concise way of writing the number of unique size-k combinations (each of which is called a k-combination) which can be made from n different objects. It turns out from inspection that the coefficient in from of a term in the multiplication (a+b)(a+b), say the term ab, is equal to C(n,k), where n = 2 (the order of the term - ab is an order 2 term), and k = 1 (the power on one of the terms - will be explained shortly). This gives C(2,1) = 2!/(1!1!) = 2, meaning that the product ab shows up 2 times in the process of doing the multiplication shown above. To give a more complex example and to better illustrate how this works, consider doing the product (a+b)(a+b)(a+b). What if I wanted to know what the coefficient would be on the a2 b term? Identify n and k first. Here, n = 3 since the order of the term is 3. In this case, the powers on the individual terms a and b are different, but see what happens if you pick k = 2 (for a) and k = 1 (for b) in separate calculations. First, C(3,2) = 3!/(2!(3-2)!) = 3. If we try it with k = 1, we get C(3,1) = 3!/(1!(3-1)!) = 3 as well! So regardless of which variable of which we choose to use the power for k, we get that the coefficient is equal to 3. In short, you can choose either and you will get the right answer. So finally, how does this allow you to calculate a polynomial product? All you have to do is think of all of the combinations of terms that might come from the multiplication. (a+b)(a+b)(a+b) gives the following: a3, a2 b, ab2, and b3. Once you write these down, you need only sum them with their appropriate coefficients. (a+b)(a+b)(a+b) = C(3,3) a3 + C(3,2)a2 b + C(3,1)ab2 + C(3,0)b3 = a3 + 3a2 b + 3ab2 + b3 Just remember that 0! = 1 (for calculating C(3,0)). This is obviously true because we need C(3,3) = C(3,0) since on this last term (b3), we can choose the power on either variable (the power on a being 0 since a0 = 1) and in both cases the coefficient must be the same. This method may also be used for polynomials with more than 2 terms each. An example is (a+b+c)(a+b+c). This topic falls under the area of combinatorics, which is quite interesting in its own right. Enjoy.

User Avatar

Wiki User

βˆ™ 16y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: What is the correct method for squaring a binomial?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

How can you introduce squaring a binomial to the learners?

You could start with multiplying two different binomials ("FOIL" and such), then squaring a binomial is just a special case. In both cases, you could give a geometric illustration (a square with sides a+b and c+d, and the product represented by area)


How do you solve a square of a binomials?

Squaring a binomial can be done by writing the binomial twice and multiply using FOIL method.EX: (x+3)2 = (x+3)(x+3) = x2 +3x +3x +9 = x2 + 6x +9


What is the correct way to write the binomial scientific name for red maple?

The correct binomial scientific name for red maple is Acer rubrum.


The binomial system of nomenclature was developed by?

The binomial system if nomenclature was developed by Carolus Linnaeus. This is the naming method using the genus and species of an organism.


What are the steps in squaring a binomials?

Squaring a binomial is just a mater of taking the binomial times itself, for example(a+b)2=(a+b)*(a+b)Here you apply FOIL technique, meaning: First, Outer, Inner and Last -- see below(a*a)+(a*b)+(b*a)+(b*b)Observing that (a*b)=(b*a) in alegbra the above equation can be rewritten as:a2+2ab+b2yeah!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!thank you for watching wowowee@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ the "F.O.I.L" way is the best solution and the easiest!


Match each binomial expression with the set of coefficients of the terms obtained by expanding the expression. Note: Each set of coefficients is listed in the correct order?

Binomial sometimes can extend to get the right results or correct order


Method of classifying organisms using a two-name system?

The binomial classification system.


What are the advantages of foil method?

The foil method is a straightforward way to multiply two binomials quickly and accurately. It ensures all terms in the product are accounted for by multiplying each term in the first binomial by each term in the second binomial. This method is especially useful when dealing with simple polynomial multiplication.


What is the correct format for the binomial name human being?

The correct binomial name for the human being is Homo sapiens. It consists of the genus name (Homo) capitalized and the species name (sapiens) in lowercase, both italicized in scientific writing.


Is this number a monomial or binomial or trinomial 30x6-1?

Binomial. Binomial. Binomial. Binomial.


What increase faster doubling a number or squaring?

Squaring. Doubling is only multiplying a number by 2, whereas, squaring is multiplying a number by itself :)


What is the two method to findthe product of binomial?

FOILMultiply First Outer Inner LastThen add the outer and inner.