5 Questions
What is the product of the sum and difference of two terms x and y?
$x^2 - y^2$
What is the algebraic identity for the square of a binomial (x + y)?
$x^2 + 2xy + y^2$
What is the algebraic identity for the square of a binomial (x - y)?
$x^2 - 2xy + y^2$
What is the general form of a polynomial in one variable?
$a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$
What is the correct definition of a variable in algebra?
A symbol that can take any real value
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.
Test your knowledge of polynomial expressions, factorization, and algebraic identities with this quiz on Chapter 2 "Polynomials" from the mathematics syllabus. Practice applying the algebraic identities (x + y)2, (x – y)2, and x2 – y2 to factorize expressions.
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