Podcast
Questions and Answers
What is the result of (11x + 11)(8x + 4)?
What is the result of (11x + 11)(8x + 4)?
88x^2 + 132x + 44
What is the result of (7x + 8)(5x + 2)?
What is the result of (7x + 8)(5x + 2)?
35x^2 + 54x + 16
What is the result of (7x + 11)(8x + 4)?
What is the result of (7x + 11)(8x + 4)?
56x^2 + 116x + 44
What is the result of (7x + 12)(10x + 7)?
What is the result of (7x + 12)(10x + 7)?
What is the result of (-9x + 3)(6x - 8)?
What is the result of (-9x + 3)(6x - 8)?
What is the result of (-5x - 4)(-2x + 3)?
What is the result of (-5x - 4)(-2x + 3)?
What is the result of (12x + 8)(6x + 5)?
What is the result of (12x + 8)(6x + 5)?
What is the result of (10x + 10)(-10x + 4)?
What is the result of (10x + 10)(-10x + 4)?
What is the result of (-8x - 9)(-2x - 4)?
What is the result of (-8x - 9)(-2x - 4)?
What is the result of (-2x + 5)(-9x + 10)?
What is the result of (-2x + 5)(-9x + 10)?
What is the result of (12x + 16)(9x - 8)?
What is the result of (12x + 16)(9x - 8)?
What is the result of (10x - 6)(-18x - 17)?
What is the result of (10x - 6)(-18x - 17)?
What is the result of (-12x - 9)(-15x + 10)?
What is the result of (-12x - 9)(-15x + 10)?
What is the result of (-20x + 6)(16x + 17)?
What is the result of (-20x + 6)(16x + 17)?
What is the result of (-6x + 14)(16x - 20)?
What is the result of (-6x + 14)(16x - 20)?
What is the result of (-20x - 12)(7x - 12)?
What is the result of (-20x - 12)(7x - 12)?
What is the result of (6x + 12)(-10x + 8)?
What is the result of (6x + 12)(-10x + 8)?
What is the result of (-15x + 12)(-9x - 7)?
What is the result of (-15x + 12)(-9x - 7)?
What is the result of (9x - 12)(9x - 13)?
What is the result of (9x - 12)(9x - 13)?
What is the result of (20x - 19)(-10x - 12)?
What is the result of (20x - 19)(-10x - 12)?
What is the value of 3^3?
What is the value of 3^3?
What is the value of 2^2?
What is the value of 2^2?
What is the value of 4^0?
What is the value of 4^0?
What is the value of 6^0?
What is the value of 6^0?
What is the value of 6^2?
What is the value of 6^2?
What is the value of 5^3?
What is the value of 5^3?
What is the value of (-4)^0?
What is the value of (-4)^0?
What is the value of (-3)^2?
What is the value of (-3)^2?
What is the value of 6^-4?
What is the value of 6^-4?
What is the value of (-2)^-3?
What is the value of (-2)^-3?
What is the value of (-2)^-2?
What is the value of (-2)^-2?
What is the value of 5^-3?
What is the value of 5^-3?
What is the value of 0.5^-2?
What is the value of 0.5^-2?
What is the value of 0.07^4?
What is the value of 0.07^4?
What is the value of 0.09^3?
What is the value of 0.09^3?
What is the value of 1.2^-1?
What is the value of 1.2^-1?
What is the value of (-8)^-3?
What is the value of (-8)^-3?
What is the value of (-0.1)^2?
What is the value of (-0.1)^2?
What is the value of [2/4]^3?
What is the value of [2/4]^3?
What is the value of [-2/3]^-1?
What is the value of [-2/3]^-1?
What is the value of 0.05^-2?
What is the value of 0.05^-2?
What is the value of [-8/12]^-3?
What is the value of [-8/12]^-3?
What is the value of (-0.12)^4?
What is the value of (-0.12)^4?
What is the value of (-0.6)^-3?
What is the value of (-0.6)^-3?
What is the value of [5/12]^1?
What is the value of [5/12]^1?
What is the value of 0.02^-1?
What is the value of 0.02^-1?
What is the value of (-0.8)^2?
What is the value of (-0.8)^2?
What is the value of [2/4]^1?
What is the value of [2/4]^1?
What is the value of (-0.09)^-2?
What is the value of (-0.09)^-2?
What is the value of [5/6]^3?
What is the value of [5/6]^3?
What is the value of [5/10]^-3?
What is the value of [5/10]^-3?
What is the value of (-0.09)^3?
What is the value of (-0.09)^3?
Flashcards are hidden until you start studying
Study Notes
Polynomial Multiplication
- Expressions involving binomials can be expanded using the distributive property.
- For example, multiplying (11x + 11)(8x + 4) results in 88x² + 132x + 44.
- Expanding (7x + 8)(5x + 2) results in a polynomial 35x² + 54x + 16.
- Knowing how to multiply coefficients and add exponents is crucial for these calculations.
Special Products
- When multiplying binomials with both positive and negative coefficients, such as (-9x + 3)(6x - 8), the output is -54x² + 90x - 24.
- Negative signs can significantly affect the product, demonstrated by multiplying (-20x + 6)(16x + 17) yielding -320x² - 244x + 102.
Exponents and Powers
- Exponents represent repeated multiplication of a base number; for example, 3³ equals 27.
- Any non-zero number raised to the power of zero equals one, e.g., 4⁰ = 1 and 6⁰ = 1.
- Negative exponents represent reciprocal values; for instance, 6⁻⁴ = 1/1296.
Special Cases with Negative Bases
- Negative bases raised to even powers result in positive outcomes, such as (-3)² = 9.
- When negative bases are raised to negative powers, the result is a negative fraction: (-2)⁻³ = -1/8.
Fractional and Decimal Exponents
- Exponentiation can also be applied to fractions and decimals; for example, (2/4)³ = 1/8.
- The process works similarly for decimals: 0.05⁻² equals 400.
Key Fractional Outcomes
- When raising fractions to negative powers, the expression's outcome is the reciprocal of the base raised to the opposite power, like [-2/3]⁻¹ = -3/2 or -1 1/2.
- Raising fractions like [5/10]⁻³ results in a whole value: 8/1 = 8.
Conclusions on Calculations
- Careful execution of polynomial multiplication and exponent rules leads to accurate results essential in algebra.
- Understanding these concepts lays the groundwork for more advanced algebraic expressions and computations.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
