Question

How would the expression x^2-9 be written using difference of swuares

Answer 1

(x+3)(x-3)

x squared and -9 are both square numbers.

the square root of x^2 is x

the square root of -9 is 3. so you just need to write (x+3)(x-3)

you can check by expanding the brackets and the middle x terms should cancel out

Answer 2

(x-3)(x+3)

Explanation:

Here we have to represent our algebraic expression as difference of square.

In order to do so we have use the formula given under.

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

Hence first we have to guess the square root of the 9 , which is 3 and represent our numeric term in our expression as square of it.

Hence

`(x^2-9)\\= (x^2-3^2)`

Now we apply the formula

`(x^2-3^2)=(x-3)(x+3)`

Hence the above expression is our answer.