8 Questions
What is the simplified form of the expression 3(x + 2) - 4(x - 1)?
-x + 5
What is the simplified form of the polynomial expression (2x^3 + x^2) - (x^3 - 3x^2)?
x^3 + 4x^2
What is the simplified form of the complex expression (3 + 2i) + (1 - 4i)?
4 - 2i
What is the simplified form of the radical expression 18 + 2√2?
3√2 + 2√2
What is the simplified form of the rational expression 3x^4 ÷ x^2?
3/4
What is the expanded form of the logarithmic expression log(ab)?
loga + logb
What is the rationalized form of the expression 1/√3?
√3/3
What is the domain of the function f(x) = 1/(x - 3)?
x ≠ 3
Study Notes
Algebraic Expressions
- Simplify the expression 3(x+2) - 4(x-1) to get -x + 5
- Simplify the polynomial expression (2x^3 + x^2) - (x^3 - 3x^2) to get x^3 + 4x^2
Complex Numbers
- Simplify the expression (3 + 2i) + (1 - 4i) to get 4 - 2i
Radical Expressions
- Simplify the radical expression 18 + 2√2 to get 3√2 + 2√2
Rational Expressions
- Simplify the rational expression 3x^4 ÷ x^2/4 to get 3/2
Logarithmic Expressions
- Expand the logarithmic expression log(ab) to get loga + logb
Rationalizing Denominators
- Rationalize the denominator of 1/√3 to get √3/3
- Rationalize the expression 2/√1 + 2 to get 2(1 - √2)
Domain and Range
- Find the domain of the function f(x) = 1/(x - 3) to get x ≠ 3
Simplify the algebraic expressions and choose the correct answer from the options.
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