What makes these products 'special'?The algebraic products on this page are used all the time later in this chapter, and in a lot of the math you will come across later. They are 'special' because they are very common, and they're worth knowing.If you can recognize these products easily, it makes your life easier later on. Special Products involving SquaresThe following special products come from multiplying out the brackets. You'll need these often, so it's worth knowing them well.a( x + y) = ax + ay (Distributive Law)( x + y)( x − y) = x 2 − y 2 (Difference of 2 squares)( x + y) 2 = x 2 + 2 xy + y 2 (Square of a sum)( x − y) 2 = x 2 − 2 xy + y 2 (Square of a difference) Examples using the special productsExample 1: Multiply out 2 x( a − 3)Answer. To expand this, we put it in the form ( a + b) 2 and expand it using the third rule above, which says:( a + b) 2 = a 2 + 2 ab + b 2I puta = x + 2b = 3 yThis gives me:( x + 2 + 3 y) 2This is the ( a + b) 2 step.= ( x + 2 + 3 y) 2= x + 2 2 + 2 x + 2(3 y) + (3 y) 2Here I apply: ( a + b) 2 = a 2 + 2 ab + b 2= x 2 + 4 x + 4 + (2 x + 4)(3 y) + 9 y 2In this row I just expand out the brackets.= x 2 + 4 x + 4 + 6 xy + 12 y + 9 y 2This is a 'tidy up' step.I could have chosen the following and obtained the same answer:a = xb = 2 + 3 yTry it!
Special Products involving CubesThe following products are just the result of multiplying out the brackets.( x + y) 3 = x 3 + 3 x 2 y + 3 xy 2 + y 3 (Cube of a sum)( x − y) 3 = x 3 − 3 x 2 y + 3 xy 2 − y 3 (Cube of a difference)( x + y)( x 2 − xy + y 2) = x 3 + y 3 (Sum of 2 cubes)( x − y)( x 2 + xy + y 2) = x 3 − y 3 (Difference of 2 cubes)These are also worth knowing well enough so you recognize the form, and the differences between each of them. Because it's easier than multiplying out the brackets and it helps us solve more complex algebra problems later.)Example 8: Expand (2 s + 3) 3Answer.
Special Products And Factoring Pdf Software
This is factored in a similar fashion to the sum of twocubes.Note the only difference is that the sign in the binomial is a - whichmatches the original sign, and the sign in front of ax is positive,whichis the opposite sign.The difference of two cubes has to be exactly in thisform to use thisrule. When you have the difference of two cubes, you have aproductof a binomial and a trinomial. The binomial is the difference ofthe bases that are being cubed.
Special Products And Factoring Pdf Example
The trinomial is the first basesquared,the second term is the opposite of the product of the two bases found,and the third term is the second base squared. These are practice problems to help bring you to thenext level.It will allow you to check and see if you have an understanding ofthesetypes of problems. Math works just likeanythingelse, if you want to get good at it, then you need to practiceit.Even the best athletes and musicians had help along the way and lots ofpractice, practice, practice, to get good at their sport or instrument.In fact there is no such thing as too much practice.To get the most out of these, you should work theproblem out onyour own and then check your answer by clicking on the link for theanswer/discussionfor that problem. At the link you will find the answeras well as any steps that went into finding that answer.PracticeProblems 1a - 1e: Factor Completely.
Brooks, Simon (2017) 2015. 
Abergavenny Chronicle. Retrieved 12 August 2019. Olding, Frank (7 January 2016).