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 51

Capitolo 1, Problema 51

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

Guida verificata passo dopo passo

Recognize that the expression is a product of two binomials in the form $(a - b)(a + b)$, where $a = 4x^{2}$ and $b = 5y$.

Recall the difference of squares formula: $(a - b)(a + b) = a^{2} - b^{2}$.

Apply the formula by squaring each term: calculate $a^{2} = (4x^{2})^{2}$ and $b^{2} = (5y)^{2}$.

Write the expression as $a^{2} - b^{2}$, which becomes $(4x^{2})^{2} - (5y)^{2}$.

Simplify the squares by applying the exponent rules: $(4x^{2})^{2} = 4^{2} imes (x^{2})^{2}$ and $(5y)^{2} = 5^{2} imes y^{2}$.

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Difference of Squares

The difference of squares is a special product formula: (a - b)(a + b) = a² - b². It simplifies the multiplication of two binomials that are conjugates by subtracting the square of the second term from the square of the first.

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Sum and Difference of Tangent

Polynomial Multiplication

Polynomial multiplication involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. This process is essential for expanding expressions and simplifying products.

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Introduction to Quadratic Equations

Exponents and Like Terms

Understanding exponents is crucial when squaring terms like 4x², which becomes (4x²)² = 16x⁴. Combining like terms means adding or subtracting terms with the same variable and exponent to simplify the final expression.

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Introduction to Inverse Trig Functions

Pratica correlata

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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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Give (a) the additive inverse and (b) the absolute value of each number. 0.16

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Determine whether each function is even, odd, or neither. See Example 5. ƒ(x) = 0.5x⁴ - 2x² + 6

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Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5