Which of the following expressions corresponds to the algebraic identity (a+b)^2?

The expression that corresponds to the algebraic identity ((a + b)^2) is derived from expanding the binomial. When you expand ((a + b)(a + b)), you apply the distributive property, also known as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial.

First, (a) is multiplied by (a), which gives you (a^2). Next, (a) is multiplied by (b), resulting in (ab). This is done again where (b) is multiplied by (a) (another (ab)), and finally (b) is multiplied by (b) which gives you (b^2). Therefore, when you combine all of these terms, you get:

• (a^2) from the first multiplication,

• (ab) from the (a \times b),

• (ab) from the (b \times a) (which adds up to (2ab)),

• (b^2) from the second multiplication.

Combining these results leads to the expression (a^2