Could William have conqured Scotland?

[Yoni]

From Wikipedia:
In 1072, he invaded Scotland, defeating Malcolm, who had recently invaded the north of England. William and Malcolm agreed to a peace by signing the Treaty of Abernethy and Malcolm gave up his son Duncan as a hostage for the peace.[12] In 1074, Edgar Ætheling submitted definitively to William.

Why did he sign a peace deal?couldn't he have conqured Scotland after Malcolm's defeat?

[Londinium]

In essence Scotland just wasn't worth it. William was having trouble holding down England, especially the North, and only had a limited number of men. He also had to keep an eye on Normandy for any trouble brewing there and it was ultimately campaigning in France where he died.

Scotland during this period was a poor frontier land without any real incentive to impose direct rule over it. The odd Anglo Saxon King had a few battles with the Scots and a few even reduced the Scots to the state of a vassal state. However it wasn't worth a full fledged campaign of subjugation for what you'd gain from it, pretty much the same reason why the Romans never fully committed to conquering Scotland after Agricola.

[Nik]

Did William have any claim to the scottish crown? Not to speak of having a claim comparable to the line of the incumbent scottish king?
Without it, his chances of assuming the throne of another country would have been slim.
Medieval wars were not total wars, if you wanted to conquer a kingdom, you needed a claim to the throne, either by blood, heritage or by marriage, anyhting else would have been an attack on Gods Order of the christian world, i.e. big NoNo

[Londinium]

Did William have any claim to the scottish crown? Not to speak of having a claim comparable to the line of the incumbent scottish king?
Without it, his chances of assuming the throne of another country would have been slim.
Medieval wars were not total wars, if you wanted to conquer a kingdom, you needed a claim to the throne, either by blood, heritage or by marriage, anyhting else would have been an attack on Gods Order of the christian world, i.e. big NoNo

Not always, William was the descendant of Vikings and Vikings had little issue with just raping and pillaging whatever they wanted to. Thats how they created Normandy to start with. There was also loads of little petty wars in France at this time, many involving the Normans. Had William wished to fabricate a reason to attack Scotland, he could have. After all at various periods in the Anglo-Saxon period Scotland was a vassal of the English, he could have demanded homage from the Scottish Kings and attacked them if they refused.

[Ardruire Iacób]

he could have demanded homage from the Scottish Kings and attacked them if they refused.

He did in 1072, and they gave it.

[Nik]

Rollo received the fief of normandy by the french king, on one hand acknowledging their power, but also to employ their prowess to defend the coastlands against other lands. Non the less, his claim to normandy was officialized by the crown.

. Had William wished to fabricate a reason to attack Scotland, he could have.

I agree, he could have. And he did invade scotland after he crushed norhhumbria and bought of the danish fleet. But "attacking" is not equal to "conquering". He defeated the scottish king Malcolm, and even received his son has hostage, but he did not have any angle to take the throne.
Look at the wars 200 later. Eduard had garrisons in scotland, and even had John Baliol as hostage/guest, forcing him to give hommage, but he never tried to take the throne for himself, because he had no claim to the throne.

[Landsknecht_88]

From Wikipedia:
In 1072, he invaded Scotland, defeating Malcolm, who had recently invaded the north of England. William and Malcolm agreed to a peace by signing the Treaty of Abernethy and Malcolm gave up his son Duncan as a hostage for the peace.[12] In 1074, Edgar Ætheling submitted definitively to William.

Why did he sign a peace deal?couldn't he have conqured Scotland after Malcolm's defeat?

Because an annexation would likely have been met with hostility from foreign powers. Naturally they would have perceived him as a threat. Besides that, he would have needed the support from the Scottish Aristocracy to maintain his power there.

[removeduser_487563287433]

The normans were far more bothered about controlling their northern Saxon subjects and their welsh Borders at this point.

[konny]

William indeed not was in the situation to make further conquests into Scotland. Not only was England still far from being "pacified", but also the situation in France required his full attention. The major target of the campaign of 1072 probably was to break the alliance between Malcolm and Edgar Ætheling.

Also "defeating the king of Scotland" did not mean to gain control over Scotland. The authority of the kingdom of Scotland in those days was mostly limited to the western Lowlands. The Highlands and the east were more or less independent. That way, with annexing Malcolm's kingdom the maximum William could have achieved was to push the instable border a bit further north - and that by the costs of a much prolonged campaign.