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Questions and Answers
What is the result of the expression (5x^2+6)-(3x^2-8)?
What is the result of the expression (5x^2+6)-(3x^2-8)?
2x+14
What is the result of the expression (6x^5-3x^64+x+1)-(8x^5+3x^4-1)?
What is the result of the expression (6x^5-3x^64+x+1)-(8x^5+3x^4-1)?
-2x^5-6x^4+x+2
What is the result of the expression (5x^4+6x^3-9x^2)-(-6x^4-6x^3+8x)?
What is the result of the expression (5x^4+6x^3-9x^2)-(-6x^4-6x^3+8x)?
11x^4+12x^3
What is the result of the expression (x^5y^2-x^3y^2+xy-1)-(x^5y^2-x^4y^2-x^3y^2-x^2y+xy-1)?
What is the result of the expression (x^5y^2-x^3y^2+xy-1)-(x^5y^2-x^4y^2-x^3y^2-x^2y+xy-1)?
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What is the result of 2^4*2^3?
What is the result of 2^4*2^3?
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What is the result of 7^5/7^2?
What is the result of 7^5/7^2?
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What is the result of (-2)^4(-2)^2?
What is the result of (-2)^4(-2)^2?
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What is the result of x^5*x^3 when x=2?
What is the result of x^5*x^3 when x=2?
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What is the result of (-4m^2n^5)^3/(3)?
What is the result of (-4m^2n^5)^3/(3)?
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Express 7% as a decimal.
Express 7% as a decimal.
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What are the absolute values of |x|=5?
What are the absolute values of |x|=5?
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What are the solutions of -9+3|y|=24?
What are the solutions of -9+3|y|=24?
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Is -6 a solution of a > -4?
Is -6 a solution of a > -4?
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Is 0 a solution of a > -4?
Is 0 a solution of a > -4?
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If a car uses 32L of gas to travel 450 km, how many liters would be required to drive 800 km (to the nearest tenth)?
If a car uses 32L of gas to travel 450 km, how many liters would be required to drive 800 km (to the nearest tenth)?
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What is the result of 3x(-x+5)?
What is the result of 3x(-x+5)?
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What is the result of 4z^2(3x+6)?
What is the result of 4z^2(3x+6)?
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What is the result of -6m^2(m^2+x)?
What is the result of -6m^2(m^2+x)?
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What is the result of -7h^4(k^6-k^4-k^3+k)?
What is the result of -7h^4(k^6-k^4-k^3+k)?
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What is the result of 2a(-5a^8b+a^2-12ab)?
What is the result of 2a(-5a^8b+a^2-12ab)?
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What is the result of (x+1)(x^2+3)?
What is the result of (x+1)(x^2+3)?
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What is the result of (x-1/4)(x+1/4)?
What is the result of (x-1/4)(x+1/4)?
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What is the result of 6(z-5)1.8?
What is the result of 6(z-5)1.8?
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Solve the inequality 3x/5 > -15.
Solve the inequality 3x/5 > -15.
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Solve the inequality 11-x > 5 + 2x/5.
Solve the inequality 11-x > 5 + 2x/5.
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Study Notes
Polynomial Operations
- Simplifying polynomials involves combining like terms and applying distributive properties.
- For the expression (5x^2+6)-(3x^2-8), the result after simplification is 2x + 14.
- The expression (6x^5-3x^4+x+1)-(8x^5+3x^4-1) simplifies to -2x^5 - 6x^4 + x + 2.
Higher-Degree Polynomials
- Combining polynomials with higher degrees requires careful tracking of each term.
- The expression (5x^4+6x^3-9x^2)-(-6x^4-6x^3+8x) simplifies to 11x^4 + 12x^3.
Multivariable Expressions
- Involving variables such as (x^5y^2-x^3y^2+xy-1)-(x^5y^2-x^4y^2-x^3y^2-x^2y+xy-1) simplifies to x^4y^2 + x^2y.
Exponents and Powers
- The product of powers can be expressed as 2^4 * 2^3 = 2^7.
- Division of powers: 7^5 / 7^2 reduces to 7^3.
- Multiplying powers: (-2)^4 * (-2)^2 results in 64.
Evaluating Expressions
- For x=2 in x^5*x^3, the evaluation yields 256.
- Evaluating powers can sometimes lead to fractions or negative numbers.
Absolute Values
- The absolute value equation |x| = 5 has solutions 5 and -5.
- The equation -9 + 3|y| = 24 gives solutions 11 and -11.
Inequalities and Solutions
- Testing numbers against inequalities: -6 does not satisfy a > -4, while 0 does.
Applications in Real Life
- A car consuming 32L to travel 450 km will need 56.9L for 800 km.
Algebraic Expansion
- Simple algebraic expressions expand using the distributive property.
- For example, 3x(-x + 5) simplifies to -3x^2 + 15x.
- Additionally, 4z^2(3x + 6) expands to 12x^3 + 24x^2.
Factorization
- (x + 1)(x^2 + 3) expands into x^3 + x^2 + 3x + 3.
- Factorization also applies to smaller expressions like (x - 1/4)(x + 1/4), which yields x^2 - 1/16.
Solving Inequalities
- Solving the inequality 3x/5 > -15 leads to x > -25.
- For 11 - x > 5 + 2x/5, you find equivalent expressions or bounds for x.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your skills with these challenging math problems. Each flashcard presents a unique problem that requires you to simplify complex expressions in algebra. Perfect for students looking to reinforce their math knowledge and problem-solving abilities.
