Question

The product of (a + b)(a − b) is a2 − b2. (1 point) Sometimes Always Never

Answer 1

ANSWER

$\boxed{Always}$
EXPLANATION


The given product is

$( a - b)(a + b)$

This is always equal to

${a}^{2} - {b}^{2}$


The identity

$( a - b)(a + b) = {a}^{2} - {b}^{2}$


is called difference of two squares.


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


$( a - b)(a + b) = a(a + b) - b(a + b)$



$( a - b)(a + b) = {a}^{2} + ab - ab- {b}^{2}$

This simplifies to

$( a - b)(a + b) = {a}^{2} - {b}^{2}$

Answer 2

Answer:

The product of $(a + b)(a-b)\ \text{is}\ a^2-b^2$ is always true.

Step-by-step explanation:

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

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  ⇒ $a^2-b^2=(3)^2-(2)^2=9-4=5$.

Since, LHS = RHS ,

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