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ANSWER

[tex]\boxed{Always}[/tex]
EXPLANATION


The given product is

[tex]( a - b)(a + b)[/tex]

This is always equal to

[tex] {a}^{2} - {b}^{2} [/tex]


The identity

[tex]( a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]


is called difference of two squares.


We can verify this by simply expanding the brackets using the distributive property to obtain,


[tex]( a - b)(a + b) = a(a + b) - b(a + b)[/tex]



[tex]( a - b)(a + b) = {a}^{2} + ab - ab- {b}^{2} [/tex]

This simplifies to

[tex]( a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]

Answer:

The product of [tex](a + b)(a-b)\ \text{is}\ a^2-b^2[/tex] is always true.

Step-by-step explanation:

Given : A statement that the product of [tex](a + b)(a-b)\ \text{is}\ a^2-b^2[/tex].

We have to check that above statement is always true, sometimes or never.

Let us take some values for a and b and then check whether the left hand side is equal to right hand side,

Let a = 3  and b = 2

Then left side ⇒ (a + b) (a - b) = (3 + 2) (3 - 2) = (5)(1) = 5

Also Right side  ⇒ [tex]a^2-b^2=(3)^2-(2)^2=9-4=5[/tex].

Since, LHS = RHS ,

Thus, the product of [tex](a + b)(a-b)\ \text{is}\ a^2-b^2[/tex] is always true.

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