product category and taxonomy

Hey,

I’d like to display the widget on a product_category (woocommerce) and his childrens. Let’s imagine i want to display the widget on childrens of category 1

I have tried this but does,doesn’t work.

is_product_category() && in_array($cat, get_term_children(1))

the same question with several category. I want to display the widget on childrens of category 1, 2, 3, 4

is_product_category() && in_array($cat, get_term_children(1,2,3,4))

Thanks for your help