Multiply 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 multiply each term in one polynomial by each term in another 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 result of multiplying (a + b)(c + d)?

Back

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

Front

How do you simplify the expression -3x²(7x² - x + 4)?

Back

The simplified expression is -21x⁴ + 3x³ - 12x².

Front

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

Back

The product is 2x³ + 11x² + 14x + 3.

Front

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

Back

The result is 4x² - 9, which is a difference of squares.

Front

How do you expand (x + 5)²?

Back

The expansion is x² + 10x + 25, using the formula (a + b)² = a² + 2ab + b².

Front

What is the result of (x - 3)(x² + 2x + 7)?

Back

The result is x³ - x² + x - 21.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (x + 5) or (2x - 3).