Question

Explain why the products (x-3)^2 and (x+3)(x-3) have a different number of terms

Answer 1

We know that these products are

`\begin{gathered} (x-3)^2=x^2-6x+9 \\ (x+3)(x-3)=x^2-9 \end{gathered}`

The first product has three terms because the square power of a binomial will always have three terms given that it follows the following rule

`(a-b)^2=a^2-2ab+b^2`

The second product has just two terms because it's not the binomial to the square but it's a perfect square difference that follows the following rule

`(a+b)(a-b)=a^2-b^2`