Many Christians and Jews mistakenly believe that Abraham's descendants through Ishmael (Muhammad and his ancestors, as seen in Fig. 3) were excluded from God's covenant with Abraham (pbuh) because Ishmael's mother, Hagar, was not a legitimate wife of Abraham, thus, her son Ishmael (the father of the Arabs) was not a legitimate son of Abraham. Therefore, they conclude that Ishmael(pbuh) and his descendants were not included in God's covenant with the sons of Abraham (pbuh) and that this covenant was exclusive to Abraham's second son, Isaac, the father of the Jews.

In what follows we will disprove each of these claims, in addition to showing evidence of human tampering with the text of the Biblical verses.

The story of Ishmael according to the Bible is as follows: Abraham married Sarah (pbut). Sarah was a barren woman and bore him no children (Genesis 16:1). God then made a great promise to Abraham even before any children were born to him.

"And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing: And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed."

Genesis 12:2-3
 

Not long after, Sarah gave Abraham her handmaid, Hagar, to be his wife according to the legal Jewish custom of polygamous marriages (customary in the Bible among Israelites and many of their prophets).

"And Sarai Abram's wife took Hagar her maid the Egyptian, after Abram had dwelt ten years in the land of Canaan, and gave her to her husband Abram to be his wife.."

Genesis 16:3

In Genesis 16 we are told that after Hagar (pbuh) became pregnant with Ishmael, Sarah (pbuh) felt that Hagar despised her, so she dealt with her harshly until she was forced to escape from this harsh treatment

"And when Sarai dealt harshly with her, she fled from her face"

Genesis 16:6.
 

The angel of God then appeared before Hagar and told her to return to Sarah and submit herself to her will and that "the Lord has heard thy affliction" and would reward her with a son called "Ishmael" (God hears) and would multiply her seed exceedingly. Hagar willingly bowed to the command of her Lord and returned and submitted herself to Sarah. In A Dictionary of Biblical tradition in English literature, we read:

"The Jewish Haggadah identifies Ishmael as one of the six men who were given a name by God before their birth (Ginzberg, LJ 1.239)."