Learning Task 2:
B. Perform the indicated operations. Simplify your answer.
1. 2ab( 4a² + 3ab - 7b²)
2. -3xy(x³y³ - 3ײy + 7xy²)
3. (x + 2)(x² -3x + 2)
4. (2x - 1)(2ײ + 4x + 3)
5. (12y² -9y + 16)(8y³ -14y + 5)
6. 25a⁵b³c
5ab⁴c
7. 16a³b²c⁵ - 24a⁵bc⁴ + 44a⁷b⁶c⁶
4a²bc³
8. 30c² + 19ac - 63a²
6c - 7a
9. (a⁶ + b⁶) ÷ (a² + b²)
10. 6w³ + 7w - 12w + 15
2w² + 3w - 5
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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:
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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