Multiplying Polynomials

This week in math class I have learned how to FOIL when multiplying polynomials as well as using an area diagram.


FOIL is a distributive technique when multiplying polynomials together.

F: First term in each bracket  (a+b)(c+d)   first term: a \cdot c

O: outside terms        (a+b)(c+d)    Outside term: a \cdot d

I: inside terms        (a+b)(c+d)     Inside term: b \cdot c

L: last term in each bracket        (a+b)(c+d)   Last term: b \cdot d


example: (a^2+8)(a^2-8)

F: First term in each bracket

You are taking a^2 and multiplying it with the other a^2 in the other bracket which will then give you a^4 because you add the exponents when the bases are the same during multiplication.


I: Inside terms

You have to make  sure to multiply the first term with the other term as well, everything that’s inside the other bracket, so in this case, a^2 will be multiplied with (-8) which will be -8a^2.

You are now left with a^4-8a^2.


O: Outside terms

You have multiplied the first term with everything in the other bracket and the inside term with the other term, you now need to do the same for the outside term. In this case, you now need to multiply 8 with a^2 which will give you 8a^2.


L: Last terms

Then you multiply 8 with the second term in the other bracket.

8(-8) = -64


Now put all the terms together in descending order by the exponents and collect like terms if needed.


-8a^2 and +8a^2 cancel out so you are now left with : a^4-64

This is Foiling but I learned a quicker technique that you can use depending on each equation.

Example: (x+7)^2

Instead of expanding the equation then simplifying, you just need to square x = x^2, then multiply x with +7 and double it = 7x \cdot 2 = 14x, then square the last digit which is 7 = 7^2 = 49. Now you are left with: = x^2+14x+49


The hardest part of this lesson was when I had to find the area of a rectangle/square when it had empty areas, so you had to find out the angles by subtracting then multiplying and other steps which was a little confusing. But I will keep practicing these equations.


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