Special products make it easier to factor polynomials as certain special patterns are formed when a polynomial has a specific group of factors. For example, if a polynomial has the…

Special products are simply special cases of multiplying certain types of binomials together. We have three special products: (a + b)(a + b) (a – b)(a – b) (a + b)(a – b)

How To: Given a binomial multiplied by a binomial with the same terms but the opposite sign, find the difference of squares.

1. Square the first term of the binomials.
2. Square the last term of the binomials.
3. Subtract the square of the last term from the square of the first term.

The trinomial x2 + 6x + 9 is a perfect square trinomial. Let’s factor this trinomial using the methods you have already seen. Factor x2 + 6x + 9. Rewrite 6x as 3x + 3x, as 3 • 3 = 9, the last term, and 3 + 3 = 6, the middle term.

The type of special product is ‘a perfect square trinomial’.

Which statement best describes Kylie’s explanation? Kylie is correct. Kylie correctly understood that it is a difference of squares, but she did not determine the product correctly. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.

Which shows a perfect square trinomial? The table represents the multiplication of two binomials. Kylie explained that (-4x + 9)^2 will result in a difference of squares because (-4x + 9)^2 = (-4x)^2 + (9)^2 = 16x^2 + 81.

The correct answer is “8ab+12a-2b-3”.

(-2m +5n)^2 is a perfect square. It expands to the trinomial 4m^2 -20mn +25n^2, a “perfect square trinomial.”

The polynomial is a perfect square.

Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

Solving this, we get that x = –2. That is, while we place the “±” sign on the side with the number, the “plus-minus” actually (technically) comes from the side with the variable, because the square root of the squared variable returns the absolute value of that variable.