Question

Find the product of (x + 3)(x − 3)

Answer 1

Let's run through the steps

1. x(x+3)+(x+3)-3    ----------------------------    Distribute
2. $x^{2} +3x-3x-9$   ---------------     Simplify
3. $x^{2} -9$   -------------------------     Simplify

Answer 2

The product of $\rm (x+3)(x-3)$ is $\rm \bold{ x^2 -9}$

The product of two algebraic terms is expressed as formulated in equation (1)

Let the first term be $\rm (a+b)$

Let the second  term be $\rm (a-b)$

The product of both the terms is given

$\rm (a+b) (a-b ) = a^2 -b^2.........(1)$

Equation (1) is an algebraic identity

This can be proved in the following way

The product of two terms is given by as formulated in equation (2)

$\rm (x+y)\times (p+q) = px +qx +py +qy......(2)$

$\rm hence, (a+b) (a-b) = a^2 -ba +ab -b^2 = a^2 -b^2$

We have to find out the product of (x + 3)(x − 3)

On comparing it with equation (1) we get

a = x

b = 3

from the equation (1) we can get

$\rm (x +3)(x-3) = x^2 -3^2 = x^2 -9$

So the product of $\rm (x+3)(x-3)$ is $\rm \bold{ x^2 -9}$  

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