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Expand the expression [tex](A+B)^2[/tex].

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Note: The second part "17: 14" appears unrelated and has been removed for clarity.

Sagot :

GinnyAnsweridn
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]
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