〜わけがない
there's no way, it can't be
Plain form + わけがない (な-adj + な · Noun + の / である)
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わけがない flatly rules something out: 彼がうそをつくわけがない, "there's no way he'd lie". There's no reason or logic that could make it true.
It's very close to はずがない (N4). わけがない is a little more common in conversation and more emotional; はずがない leans on expectations. In casual speech, が often drops: わけない.
The polite form is わけがありません.
Watch out for its lookalikes: わけではない is "it's not that…" (a partial denial), and わけにはいかない is "I can't, given the situation". Only わけがない means "no way".
Examples
こんな難しい問題、私に解けるわけがない。
There's no way I can solve a problem this hard.
彼がうそをつくわけがない。
There's no way he'd lie.
一日で終わるわけがないよ。
There's no way it'll be done in a day.
そんな安い値段で買えるわけがありません。
There's no way you can buy it that cheaply.
知らないわけがない。毎日会っているんだから。
There's no way they don't know. They see each other every day.