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

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 114

Chapter 1, Problem 114

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

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.

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.

Calculate the squares $x^2$ and $y^2$ separately by squaring the substituted values: \$63^2$ and $57^2$.

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.

Simplify the resulting expression step-by-step to find the final value of the expression without directly multiplying the original binomials.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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