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Questions and Answers
What is the product of the sum and difference of two terms x and y?
What is the product of the sum and difference of two terms x and y?
- $x^3 + y^3$
- $x^2 + y^2$
- $x^2 - y^2$ (correct)
- $x^3 - y^3$
What is the algebraic identity for the square of a binomial (x + y)?
What is the algebraic identity for the square of a binomial (x + y)?
- $x^3 - 3x^2y + 3xy^2 - y^3$
- $x^2 - 2xy + y^2$
- $x^3 + 3x^2y + 3xy^2 + y^3$
- $x^2 + 2xy + y^2$ (correct)
What is the algebraic identity for the square of a binomial (x - y)?
What is the algebraic identity for the square of a binomial (x - y)?
- $x^2 + 2xy + y^2$
- $x^3 + 3x^2y + 3xy^2 + y^3$
- $x^3 - 3x^2y + 3xy^2 - y^3$
- $x^2 - 2xy + y^2$ (correct)
What is the general form of a polynomial in one variable?
What is the general form of a polynomial in one variable?
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What is the correct definition of a variable in algebra?
What is the correct definition of a variable in algebra?
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Study Notes
Algebraic Identities and Polynomials
- The product of the sum and difference of two terms x and y is (x + y)(x - y) = x² - y².
Squares of Binomials
- The algebraic identity for the square of a binomial (x + y) is (x + y)² = x² + 2xy + y².
- The algebraic identity for the square of a binomial (x - y) is (x - y)² = x² - 2xy + y².
Polynomials
- A polynomial in one variable is an expression consisting of variables, coefficients, and constants combined using addition, subtraction, and multiplication, but not division.
Variables in Algebra
- A variable in algebra is a symbol that represents a value that can change or vary, often represented by letters such as x, y, or z.
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