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(a3 - 2a²) -(3a² -4a³)

(a3 - 2a²) -(3a² -4a³)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The image shows a mathematical expression with annotations, possibly illustrating the process of simplifying or rearranging terms. The expression is: \[ (a^3 - 2a^2) - (3a^2 - 4a^3) \] There are curved arrows connecting terms across the expression, indicating the operation or alignment process typically used for combining like terms. The arrows can be interpreted as: 1. Connecting \(a^3\) from the first bracket to \(-4a^3\) in the second bracket. 2. Connecting \(-2a^2\) from the first bracket to \(3a^2\) in the second bracket. This type of visual annotation is used to indicate terms that should be combined due to having the same power of \(a\). The expressions are likely being simplified through the addition or subtraction of like terms.
Transcribed Image Text:The image shows a mathematical expression with annotations, possibly illustrating the process of simplifying or rearranging terms. The expression is: \[ (a^3 - 2a^2) - (3a^2 - 4a^3) \] There are curved arrows connecting terms across the expression, indicating the operation or alignment process typically used for combining like terms. The arrows can be interpreted as: 1. Connecting \(a^3\) from the first bracket to \(-4a^3\) in the second bracket. 2. Connecting \(-2a^2\) from the first bracket to \(3a^2\) in the second bracket. This type of visual annotation is used to indicate terms that should be combined due to having the same power of \(a\). The expressions are likely being simplified through the addition or subtraction of like terms.
### Expression Simplification **Problem:** Simplify the following algebraic expression: ​\( (2x^3 + 7x^2 + x) + (2x^2 - 4x - 12) \) **Explanation:** This expression is a sum of two polynomial expressions. It includes terms with varying powers of \(x\). - The first polynomial is \(2x^3 + 7x^2 + x\). - The second polynomial is \(2x^2 - 4x - 12\). **Steps to Simplify:** 1. **Combine Like Terms:** - Identify like terms across the polynomials. Like terms have the same power of \(x\). 2. **Add coefficients of like terms:** - For \(x^2\): Combine \(7x^2\) and \(2x^2\) to get \(9x^2\). - For \(x\): Combine \(x\) and \(-4x\) to get \(-3x\). - The constants are added separately, but here there is only \(-12\). 3. **Resulting Expression:** - The simplified form is \(2x^3 + 9x^2 - 3x - 12\). In the image, arrows show the process of combining like terms visually, connecting terms across the polynomial boundary.
Transcribed Image Text:### Expression Simplification **Problem:** Simplify the following algebraic expression: ​\( (2x^3 + 7x^2 + x) + (2x^2 - 4x - 12) \) **Explanation:** This expression is a sum of two polynomial expressions. It includes terms with varying powers of \(x\). - The first polynomial is \(2x^3 + 7x^2 + x\). - The second polynomial is \(2x^2 - 4x - 12\). **Steps to Simplify:** 1. **Combine Like Terms:** - Identify like terms across the polynomials. Like terms have the same power of \(x\). 2. **Add coefficients of like terms:** - For \(x^2\): Combine \(7x^2\) and \(2x^2\) to get \(9x^2\). - For \(x\): Combine \(x\) and \(-4x\) to get \(-3x\). - The constants are added separately, but here there is only \(-12\). 3. **Resulting Expression:** - The simplified form is \(2x^3 + 9x^2 - 3x - 12\). In the image, arrows show the process of combining like terms visually, connecting terms across the polynomial boundary.
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