To expand the expression [tex]\((A + B)^2\)[/tex], we use the algebraic identity for the square of a binomial. The identity states:
[tex]\[
(A + B)^2 = A^2 + 2AB + B^2
\][/tex]
Let's break this down step by step:
1. Identify the binomial: Recognize that [tex]\((A + B)\)[/tex] is the binomial that we are squaring.
2. Apply the binomial square formula: According to the identity, squaring the binomial [tex]\((A + B)\)[/tex] gives us three terms:
- The square of the first term.
- Twice the product of the two terms.
- The square of the second term.
3. Calculate each term individually:
- The square of the first term [tex]\(A\)[/tex] is: [tex]\(A^2\)[/tex].
- Twice the product of the two terms [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is: [tex]\(2AB\)[/tex].
- The square of the second term [tex]\(B\)[/tex] is: [tex]\(B^2\)[/tex].
By combining these three terms, we get:
[tex]\[
(A + B)^2 = A^2 + 2AB + B^2
\][/tex]
So, the expanded form of [tex]\((A + B)^2\)[/tex] is:
[tex]\[
A^2 + 2AB + B^2
\][/tex]
