〜わけがない
There's no way (complete negation)machine translation
FormationPlain form + わけがない (な-adjective + な, noun + の/である)
〜わけがない COMPLETELY denies a possibility: "there's no way, not a chance." The speaker relies on common sense to assert that it cannot happen: こんな難しい問題、子どもに解けるわけがない (a problem this hard — there's no way a child could solve it).
Connection: plain form + わけがない; な-adjectives add な, nouns add の or である. The polite form is わけがありません; very casual speech even shortens it to わけない.
The meaning of わけがない is very close to はずがない from N4: both mean "cannot possibly be." The difference is nuance — はずがない leans toward reasoned inference ("logically it can't be"), while わけがない carries strong emotion and is common in conversation for brushing aside an idea. And absolutely don't mix it up with わけではない: adding では flips the meaning entirely from "there's no way" (100% denial) to "it's not that…" (partial denial).
Examples
こんな難しい問題、子どもに解けるわけがない。
A problem this hard — there's no way a child could solve it.
彼がうそをつくわけがない。
There's no way he would lie.
練習もしないで上手になるわけがありません。
There's no way you'll get good without even practicing.