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. 63 x 57

Verified step by step guidance

1. Identify which special product formula applies to the given expression. Since the problem mentions both \((x+y)(x-y) = x^2 - y^2\) and \((x - y)^2 = x^2 - 2xy + y^2\), determine which one matches the expression you need to evaluate.
2. Substitute the given values \(x = 63\) and \(y = 57\) into the chosen formula. For example, if using \((x+y)(x-y)\), calculate \(x + y\) and \(x - y\) first.
3. Calculate the squares \(x^2\) and \(y^2\) separately by squaring the substituted values: \$63^2\( and \)57^2$.
4. Apply the formula by subtracting \(y^2\) from \(x^2\) if using the difference of squares formula, or by computing \(x^2 - 2xy + y^2\) if using the square of a difference formula.
5. Simplify the resulting expression step-by-step to find the final value of the expression without directly multiplying the original binomials.

Key Concepts

Difference of Squares

The difference of squares formula states that (x + y)(x - y) equals x² - y². This identity allows quick multiplication by recognizing the product as the difference between two squared terms, eliminating the need for full expansion.

Square of a Binomial

The square of a binomial, such as (x - y)², expands to x² - 2xy + y². This formula helps simplify expressions by directly applying the pattern instead of multiplying the binomial by itself step-by-step.

Substitution of Values into Algebraic Expressions

Substitution involves replacing variables with given numerical values to evaluate expressions. After applying special product formulas, substituting x = 63 and y = 57 allows calculation of the numerical result efficiently.