The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. 102^2

Verified step by step guidance

1. Recognize that 102^2 can be expressed as (100 + 2)^2.
2. Use the special product formula for a binomial square: (a + b)^2 = a^2 + 2ab + b^2.
3. Identify a = 100 and b = 2 in the expression (100 + 2)^2.
4. Substitute a and b into the formula: (100 + 2)^2 = 100^2 + 2(100)(2) + 2^2.
5. Calculate each term separately: 100^2, 2(100)(2), and 2^2, then sum them to find the result.

Key Concepts

Special Products

Special products refer to specific algebraic identities that simplify the multiplication of binomials. Common examples include the difference of squares, (a+b)(a-b) = a^2 - b^2, and the square of a binomial, (a+b)^2 = a^2 + 2ab + b^2. Understanding these identities allows for quicker calculations and simplifications in algebra.

Difference of Squares

The difference of squares is a specific case of special products where the expression takes the form (a+b)(a-b). This identity states that the product equals the square of the first term minus the square of the second term, expressed as a^2 - b^2. It is particularly useful for factoring and simplifying expressions involving squared terms.

Square of a Binomial

The square of a binomial is another important identity that states (a+b)^2 = a^2 + 2ab + b^2. This formula expands the square of a sum into three terms, which is essential for simplifying expressions and solving equations involving squared binomials. Mastery of this concept is crucial for evaluating expressions like 102^2 efficiently.