Algebra 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 the other polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you multiply a term by each term inside the parentheses.

Front

What is the product of (a + b)(a - b)?

Back

The product is a² - b², known as the difference of squares.

Front

How do you multiply a binomial by a trinomial?

Back

Multiply each term in the binomial by each term in the trinomial, then combine like terms.

Front

What is the result of (x + 2)(x + 3)?

Back

The result is x² + 5x + 6.

Front

What is the result of (2x + 3)(2x - 3)?

Back

The result is 4x² - 9.

Front

What is the result of (3x - 5)(4x² - 2x - 3)?

Back

The result is 12x³ - 26x² + x + 15.

Front

What is the result of (x + 5)(x + 4)?

Back

The result is x² + 9x + 20.

Front

What is the result of (2x + 3)(x² + 4x + 1)?

Back

The result is 2x³ + 11x² + 14x + 3.