Kahlil said that using the equation (a + b)2 = a2 + 2ab + b2, he can find a similar equation for (a - b)2. Examine his argument.
(a - b)2 = [a + (-b)]2
= a2 + 2a(-b) + (-b)2
= a2 – 2ab + b2
He is correct.
To examine Kahlil's argument, we can work through the steps he took:
1. He started with the equation (a + b)2 = a2 + 2ab + b2.
2. He wanted to find a similar equation for (a - b)2, so he replaced b with -b to get (a + (-b))2.
3. Next, he simplified (a + (-b))2 by applying the distributive property: a2 + 2a(-b) + (-b)2.
4. Finally, he simplified further: a2 - 2ab + b2.
By following these steps, he obtained the equation (a - b)2 = a2 - 2ab + b2, which is indeed a similar equation to (a + b)2.