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Operations Involving Algebraic Expressions

There are basic rational exponent laws that is applicable to standard operations. Laws of rational exponent states that when exponents are multiplied, they should be added. When exponents are divided, they should be subtracted. When an exponent is raised to another exponent they are also multiplied. If the given expression has root symbols, change them into rational exponents first.

Learning Task 2:

B.

Answers:

1. 8a³b + 6a²b² - 14ab³
2. -3x⁴y⁴ - 9x³y² - 21x²y²
3. x³ - x² - 4x + 4
4. 4x³ + 6x² + 2x - 3
5. 96y⁵ - 72y⁴ - 40y³ + 186y² - 224y + 80
6. 
7. 4abc² - 6a⁴c + 11a⁵b⁵c³
8. 5c + 9
9. a⁴ + b⁴
10. 3w - 3

Solutions:

1. 2ab( 4a² + 3ab - 7b²) = (2ab)(4a²) + (2ab)(3ab) - (2ab)(7b²)

                                      = 8a³b + 6a²b² - 14ab³

2. -3xy(x³y³ - 3ײy + 7xy²) = (-3xy)(x³y³) + (-3xy)(3x²y) + (-3xy)(7xy²)

                                         = -3x⁴y⁴ - 9x³y² - 21x²y²

3. (x + 2)(x² - 3x + 2) = (x)(x²) + (x)(-3x) + (x)(2) + (2)(x²) + (2)(-3x) + (2)(2)

                                 = x³ - 3x² + 2x + 2x² - 6x + 4

                                 = x³ - 3x² + 2x² + 2x - 6x + 4

                                 = x³ - x² - 4x + 4

4. (2x - 1)(2ײ + 4x + 3) = (2x)(2x²) + (2x)(4x) + (2x)(3) + (-1)(2x²) + (-1)(4x) + (-1)(3)

                                    = 4x³ + 8x² + 6x - 2x² - 4x - 3

                                    = 4x³ + 8x² - 2x² + 6x - 4x - 3

                                    = 4x³ + 6x² + 2x - 3

5. (12y² -9y + 16)(8y³ -14y + 5) = (12y²)(8y³) + (12y²)(-14y) + (12y²)(5) - (9y)(8y³)

                                                - (9y)(-14y) - (9y)(5) + (16)(8y³) + (16)(-14y) + (16)(5)

                                                = 96y⁵ - 168y³ + 60y² - 72y⁴ + 126y² - 45y +          

                                                   128y³ - 224y + 80

                                                = 96y⁵ - 72y⁴ - 168y³ + 128y³ + 60y² + 126y² -

                                                   224y + 80

                                                = 96y⁵ - 72y⁴ - 40y³ + 186y² - 224y + 80

6. =

7. = 4abc² - 6a⁴c + 11a⁵b⁵c³

8. = = 5c + 9

9. = a⁴ + b⁴

10. = = = 3w - 3

How to perform operations involving algebraic expressions: brainly.ph/question/10189604

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