Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to combine each term in one polynomial with each term in another polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a sum.

Front

What is the result of (a + b)(c + d)?

Back

The result is ac + ad + bc + bd, which is obtained by distributing each term.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)² is equal to a² + 2ab + b².

Front

What is the product of (x - 7)²?

Back

(x - 7)² = x² - 14x + 49.

Front

How do you multiply a monomial by a polynomial?

Back

Multiply the monomial by each term in the polynomial, distributing the monomial across all terms.

Front

What is the product of -5x⁶(3x² - 12x + 30)?

Back

-5x⁶(3x² - 12x + 30) = -15x⁸ + 60x⁷ - 150x⁶.

Front

What is the result of (2x - 1)(x + 2)?

Back

(2x - 1)(x + 2) = 2x² + 3x - 2.

Front

What is the formula for multiplying two binomials?

Back

(a + b)(c + d) = ac + ad + bc + bd.