Question

How do you multiply and simplify `\frac { 32v - 40} { v + 4} \cdot \frac { v ^ { 4} - 16v ^ { 2} } { 32v - 40}`?

Answer 1

`=v^2(v-4)`

Explanation:

You can cancel common factors.
Factorise where possible.

`cancel((32v-40))/(v+4) xx(v^4-16v^2)/cancel((32v-40))`

`=(v^2(v^2-16))/(v+4)" "larr` common factor

`=(v^2(v+4)(v-4))/(v+4)" "larr` difference of squares

`=(v^2cancel((v+4))(v-4))/cancel((v+4))`

`=v^2(v-4)`