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!