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 us to multiply a single term by each term in a sum.

Front

What is the result of multiplying (x + a)(x - a)?

Back

The result is x² - a², which is known as the difference of squares.

Front

How do you multiply a binomial by a binomial?

Back

Use the FOIL method: First, Outer, Inner, Last to find the product of two binomials.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials: multiply the First terms, the Outer terms, the Inner terms, and the Last terms, then combine like terms.

Front

What is the product of (3x + 2)(2x + 4)?

Back

The product is 6x² + 16x + 8.

Front

What is the product of (2x - 9)(2x + 9)?

Back

The product is 4x² - 81, which is the difference of squares.

Front

How do you multiply a polynomial by a monomial?

Back

Multiply each term of the polynomial by the monomial.

Front

What is the product of (5x + 2)(x² - 3x + 6)?

Back

The product is 5x³ - 13x² + 24x + 12.