Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. R - Algebra Review

Problema 53

Capitolo 1, Problema 53

Find each product. See Example 5. (4m + 2n)²

Guida verificata passo dopo passo

Recognize that the expression is a square of a binomial: \((4m + 2n)^2\). This means you will use the formula for the square of a sum: \((a + b)^2 = a^2 + 2ab + b^2\).

Identify the terms \(a\) and \(b\) in the binomial: here, \(a = 4m\) and \(b = 2n\).

Calculate the square of the first term: \(a^2 = (4m)^2 = 16m^2\).

Calculate twice the product of the two terms: \(2ab = 2 \times (4m) \times (2n) = 16mn\).

Calculate the square of the second term: \(b^2 = (2n)^2 = 4n^2\). Then, combine all parts to write the expanded form: \(16m^2 + 16mn + 4n^2\).

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Binomial Expansion

Binomial expansion involves expanding expressions raised to a power, such as (a + b)², using the formula (a + b)² = a² + 2ab + b². This allows you to rewrite the square of a sum as a sum of squares and products.

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Rationalizing Denominators Using Conjugates

Distributive Property

The distributive property states that a(b + c) = ab + ac. It is used to multiply each term inside the parentheses by the term outside, which is essential when expanding expressions like (4m + 2n)² by treating it as (4m + 2n)(4m + 2n).

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Imaginary Roots with the Square Root Property

Combining Like Terms

After expanding an expression, combining like terms means adding or subtracting terms with the same variables and exponents to simplify the expression. This step is crucial to write the final product in its simplest form.

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3:18

Adding and Subtracting Complex Numbers

Pratica correlata

Domanda del libro di testo

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (0, 0), radius 6

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Domanda del libro di testo

Add or subtract, as indicated. See Example 4. (1/a)+(b/a²)

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Domanda del libro di testo

Find each product. See Example 5. (4x² - 5y) (4x² + 5y)

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Domanda del libro di testo

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6.