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Evaluate each algebraic expression for x = 2 and y = -5. |x|+|y|
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 64
In Exercises 57–64, factor using the formula for the sum or difference of two cubes. 8x^3+125
Guida verificata passo dopo passo1
Recognize that the given expression, 8x^3 + 125, is a sum of two cubes. Recall the formula for factoring the sum of two cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2).
Identify the cube roots of each term. For 8x^3, the cube root is 2x, and for 125, the cube root is 5.
Substitute the values of a and b into the formula. Here, a = 2x and b = 5, so the expression becomes (2x + 5)((2x)^2 - (2x)(5) + (5)^2).
Simplify each term in the second factor. (2x)^2 becomes 4x^2, (2x)(5) becomes 10x, and (5)^2 becomes 25.
Write the fully factored form of the expression: (2x + 5)(4x^2 - 10x + 25).
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Sum of Cubes Formula
The sum of cubes formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2). This formula is essential for factoring expressions where two terms are perfect cubes added together, allowing for simplification and solving of polynomial equations.
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03:41
Special Products - Cube Formulas
Identifying Perfect Cubes
To apply the sum of cubes formula, it's crucial to recognize perfect cubes. A perfect cube is a number or expression that can be expressed as the cube of another number or expression, such as 8 (2^3) and 125 (5^3). Identifying these helps in correctly applying the factoring formula.
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03:41Special Products - Cube Formulas
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials. This process is fundamental in algebra as it simplifies expressions and makes it easier to solve equations. Understanding how to factor using specific formulas, like the sum of cubes, is a key skill in algebra.
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07:30Introduction to Factoring Polynomials
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