Question

How do you multiply `\frac { x ^ { 2} - 25} { 3x ^ { 5} - 15x ^ { 4} - 150x ^ { 3} } \cdot \frac { x ^ { 5} - 100x ^ { 3} } { x ^ { 2} + 5x - 50}`?

Answer 1

`1/3`

Explanation:

The first step is to factorise so you can cancel any like factors:

What can be done?

`(x^2-25)/(3x^5-15x^4-150x^3) xx (x^5-100x^3)/(x^2+5x-50)`

`"difference of squares"/"common factor" xx "common factor"/"quadratic trinomial"`

`=((x+5)(x-5))/(3x^3(x^2-5x-50)) xx (x^3(x^2-100))/((x+10)(x-5))`

`"factored"/"quadratic trinomial" xx "difference of squares"/"factored"`

`=((x+5)(x-5))/(3x^3(x-10)(x+5)) xx (x^3(x+10)(x-10))/((x+10)(x-5))`

Now cancel like factors.

`=(cancel((x+5))(cancel(x-5)))/(3cancel(x^3)cancel((x-10))cancel((x+5))) xx (cancel(x^3)cancel((x+10))cancel((x-10)))/(cancel((x+10))cancel((x-5))`

=`1/3`