Coefficient is a number or symbol multiplied by a variable in an expression. Variables without numbers have coefficient 1. Coefficients can be positive, negative, real, imaginary, or fractions
The formula (a + b)² = a² + 2ab + b² is used to find the square of a binomial. The formula can be derived by multiplying (a + b)(a + b). The geometric proof involves connecting two squares to form a rectangle
Polynomial functions are algebraic expressions with variables, coefficients, and constants. Standard form: f(x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0. Degree is highest power of variable raised to
The a³ - b³ formula is the difference of cubes formula. The formula is a³ - b³ = (a - b) (a² + ab + b²). The proof involves multiplying (a - b) with (a² + ab + b²)
Original expression: (a-b+c)² = (a-b+c)(a-b+c). Need to show identity: (a-b+c)² = a² + b² + c² - 2ab + 2ac - 2bc
Binomial is a polynomial with only two terms. Contains variable, coefficient, exponent and constant. Can be expressed as axm + bxn or ax-m + bx-n. Not all expressions with negative exponents are binomials