To evaluate an algebraic expression, determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value. Simplify the resulting expression using the order of operations. Variable is a letter that represents an unspecified number. Perform the arithmetic operations.
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Evaluating Algebraic Expressions
To evaluate an algebraic expression, determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value. Simplify the resulting expression using the order of operations. Variable is a letter that represents an unspecified number. Perform the arithmetic operations.
Learning Task 2:
Answers:
A.
B.
Solutions:
A.
1. 3abc + bc - a
a = 4 3(4)(-5)(0.6) + (-5)(0.6) - 4
b = -5 12(-3) + (-3) - 4
c = 0.6 -36 + 7 = -29
2. bxy + 5ab - ay
a = 4 (-5)(-3)(0.4) + 5(4)(-5) - (4)(0.4)
b = -5 15(0.4) + 5(-20) - 1.6
x = -3 6 - 100 - 1.6
y = 0.4 6 - 101.6 = -95.6
3. abz - 8z + b
a = 4 (4)(-5)(
) - 8(
) + (-5)
b = -5 -20(
) -
- 5
z =
-
- 5 = -10 - 4 - 5 = -19
4. ax + by - cz
a = 4 (4)(-3) + (-5)(0.4) - (0.6)(
)
b = -5 -12 - 2 -![\frac{0.6}{2} \frac{0.6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B0.6%7D%7B2%7D)
c = 0.6 -14 - 0.3 = -14.3
x = -3
y = 0.4
z =![\frac{1}{2} \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
5. 4ax + cz
a = 4 4(4)(-3) + (0.6)(
)
c = 0.6 16(-3) +![\frac{0.6}{2} \frac{0.6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B0.6%7D%7B2%7D)
x = -3 -48 + 0.3 = -47. 7
z =![\frac{1}{2} \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
6. 3x² - 2xy - 3(ab)²
a = 4 3(-3)² - 2(-3)(0.4) - 3[(4)(-5)]²
b = -5 3(9) - 6(0.4) - 3(-20)²
x = -3 27 - 2.4 - 3(400)
y = 0.4 27 - 2.4 - 1200 = 27 - 1202.4 = -1172.6
7. 25 - 2x²y + 3a²b - az²
a = 4 25 - 2(-3)²(0.4) + 3(4)²(-5) - (4)(
)²
b = -5 25 - 2(9)(0.4) + 3(16)(-5) - (4)(
)
x = -3 25 - 18(0.4) + 3(-80) -![\frac{4}{4} \frac{4}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B4%7D)
y = 0.4 25 - 7.2 - 240 - 1
z =
25 - 248.2 = -243.2
8. (az)² + 5x²y - 4bc
a = 4 [(4)(
)]² + 5(-3)²(0.4) - 4(-5)(0.6)
b = -5 (
)² + 5(9)(0.4) - 4(-3)
c = 0.6 (2)² + 45(0.4) + 12
x = -3 4 + 18 + 12 = 34
y = 0.4
z =![\frac{1}{2} \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
9. 2x²y² - 12abz - 16
a = 4 2(-3)²(0.4)² - 12(4)(-5)(
) - 16
b = -5 2(9)(1.6) - 48(
) - 16
x = -3 18(1.6) - 24(-5) - 16
y = 0.4 28.8 + 120 - 16 = 148.8 - 16 = 132.8
z =![\frac{1}{2} \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
10. 8z³ - 4x + y²
x = -3 8(
)³ - 4(-3) + (0.4)²
y = 0.4 8(
) + 12 + 1.6
z =
+ 12 + 1.6 = 1 + 12 + 1.6 = 14.6
B.
1. 5x⁴ - 3x² + 4 2. -7x³y + 4x²y² - 2 3. 24y³ - 7y² + 5
+ 6x⁴ - 4x² - 7 + 4x³y - 8x²y² + 1 + -6y³ + 7y² + 5
11x⁴ - 7x² - 3 -3x³y - 4x²y² - 1 18y³ + 10
4. 2x⁵ - 6x³ - 12x² - 4 5. 3y⁵ + y⁴ + 2y³ -2y + 5
+ -11x⁵ + 2x² + 8x + 6 + 2y⁵ + 3y³ + 9
-9x⁵ - 6x³ - 10x² + 8x + 2 5y⁵ + y⁴ + 5y³ - 2y + 14
6. 5x³ - 7x² + 3x - 4 7. 2x²y - 5xy - 3y² 8. 9x⁵ - 6x³ + 7x²
- 8x³ + 2x²+ 3x - 7 - 5x²y + 7xy - 6y² - 6x⁵ + 7x³ + 2x²
-3x³ - 9x² + 3 -3x²y - 12xy + 3y² 3x⁵ + x³ - 5x²
9. 6x² - 3x + 8 10. 1.5y³ + 4.8y² + 12
- 4x³ - 5x - 8 - y³ 1.7y² + 2y
-4x³ + 6x² + 2x + 16 .5y³ + 3.1y² + 2y + 12
How to evaluate algebraic expressions: brainly.ph/question/9744654
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