The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x²-y². On the right, (x-y)² = x²-2xy+y². Use special products to evaluate each expression. < SEE SAMPLE B> 71²

Verified step by step guidance

1. Recognize that the expression 71^2 is a perfect square, which can be evaluated using the special product formula for the square of a binomial: \((x + y)^2 = x^2 + 2xy + y^2\).
2. Rewrite 71 as a sum of two numbers that are easier to square, for example, \$71 = 70 + 1$.
3. Apply the formula \((x + y)^2 = x^2 + 2xy + y^2\) with \(x = 70\) and \(y = 1\).
4. Calculate each term separately: \(x^2 = 70^2\), \$2xy = 2 imes 70 imes 1\(, and \)y^2 = 1^2$.
5. Add the three results together to find the value of \$71^2$.

Key Concepts

Special Products Formulas

Special products are algebraic identities that simplify multiplication, such as the difference of squares (x + y)(x - y) = x² - y² and the square of a binomial (x - y)² = x² - 2xy + y². Recognizing these patterns helps quickly expand or evaluate expressions without full multiplication.

Difference of Squares

The difference of squares formula states that the product of a sum and difference of the same two terms equals the difference of their squares: (a + b)(a - b) = a² - b². This is useful for simplifying expressions and evaluating products efficiently.

Square of a Binomial

Squaring a binomial involves expanding (a ± b)² into a² ± 2ab + b². For example, (x - y)² = x² - 2xy + y². This formula allows quick calculation of squares of numbers expressed as sums or differences, such as 71² by rewriting 71 as (70 + 1).