Question

Use the information to complete the proof. Given: (a+2)^(2) Prove: (a+2)^(2)=a^(2)+4a+4

Answer 1

The proof that (a+2)^2 equals a^2 + 4a + 4 is completed by using the FOIL method to expand the squared binomial. By multiplying and then combining like terms, the final expression is achieved.

Step-by-step explanation:

To prove that (a+2)2 = a2 + 4a + 4, we will use the FOIL method, which stands for First, Outer, Inner, Last, to expand the binomial.

Here's how it is done step by step:

First, we multiply the First terms in each binomial: a × a = a2.

Next, we multiply the Outer terms: a × 2 = 2a.

Then, we multiply the Inner terms: 2 × a = 2a.

Finally, we multiply the Last terms: 2 × 2 = 4.

Now we combine all these results: a2 + 2a + 2a + 4. When we add the like terms (2a and 2a), we get 4a, which gives us the final result of a2 + 4a + 4, as required.