Well classic liberal feminist argue that, for example, the existing legal system can be used to dismantle patriarchy. Firstly it can legally oblige equal treatment of men and women, secondly it can mandate through force of law strategies to achieve better gender equity generally; for example through legally enforceable affirmative action quotas. A liberal feminist would seek to become politically engaged, and use the system to dismantle patriarchy.

Radical feminists essentially critique the legal system as being either a tool of, or at least in thrall to patriarchy. They claim that women's engagement with the legal system necessarily entails adopting the patriarchy's framework - an adversarial, classist, anti-feminist model. To successfully engage the legal system - a radical feminist argues - requires acquiescing to patriarchy. The most classic difference between liberal and radical feminism is thus often discussed in the context of engagement with the legal system, with liberal feminist arguing that it can be used to dismantle patriarchy, and radical feminists arguing that to use it requires accepting the very values of patriarchy that you're seeking to subvert.

I'm simple terms A liberal feminist would argue that more women engaging in politics will change political systems for the better. A radical feminist contends that either those women will be obliged to conform to the existing patriarchal system, or they'll be rejected; that a female leader even in a liberal democracy ultimately ends up either Margaret Thatcher - adopting all the standard patriarchal tropes - or Julia Gillard - so relentlessly hounded on gendered lines for any percieved non-conformity as to end in ultimate political failure. Thus, for the classic radical feminist, a roots-and-all approach to re-imagining politics is required before political engagement can be sucessful.