Question

determine whether each identity is true or false (a-b) (a-b) = a²-b² true or false (a+b) (a+b) =a²+2ab +b² true or false(a-b) (a-b) = a²-2ab+b² true or false(a+b) (a-b) = a²+2ab-b² true or false(a+b) (a-b) = a²-b² true or false(a+b) (a+b) = a²+b² true or false

Answer 1

false

true true

false true false

Answer 2

1)

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

we can use the distribution propertie:

`\begin{gathered} (a-b)(a-b)=a^2-ab-ab+b^2 \\ (a-b)(a-b)=a^2-2ab+b^2 \end{gathered}`

Is false

2)

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

Again, we can use the distribution propertie:

`\begin{gathered} (a+b)(a+b)=a^2+ab+ab+b^2 \\ (a+b)(a+b)=a^2+2ab+b^2 \end{gathered}`

Is true

3) is the same as the numeral 1) so in this case the experession is true

4)

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

Again, we can use the distribution propertie:

`\begin{gathered} (a+b)(a-b)=a^2-ab+ab-b^2 \\ (a+b)(a-b)=a^2-b^2 \end{gathered}`

Is false

5) is the same as the numeral 4) so in this case is true

6)

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

Using the distribution:

`\begin{gathered} (a+b)(a+b)=a^2+ab+ab+b^2 \\ (a+b)(a+b)=a^2+2ab+b^2 \end{gathered}`

So is false