Question

How do you factor `x^3-49x`?

Answer 1

Since we have `x^3`, we know that we need one `x` out and two `x` inside the parentheses.

And we know `(7)(7)` is 49. Since it is -49, one of the seven will be negative.

Thus

The answer is: `x(x+7)(x-7)`

Answer 2

`x(x+7)(x-7)`

Explanation:

We can see that both terms contain an `x` which we can factor out to get `x(x^2-49)`

Now we can use difference of two squares to factorise `x^2-49`. Difference of two squares tells us that `a^2-b^2=(a+b)(a-b)`

`x^2-49=(x+7)(x-7)` since `7^2=49`

Substituting this gives us `x(x+7)(x-7)`