Sum and Difference of Cubes

Front

What is the formula for the sum of cubes?

Back

a³ + b³ = (a + b)(a² - ab + b²)

Front

What is the formula for the difference of cubes?

Back

a³ - b³ = (a - b)(a² + ab + b²)

Front

What is a perfect square?

Back

A number that can be expressed as the square of an integer.

Front

What is a perfect cube?

Back

A number that can be expressed as the cube of an integer.

Front

Factor the difference of cubes: x³ - 27

Back

(x - 3)(x² + 3x + 9)

Front

Factor the sum of cubes: 8 + x³

Back

(x + 2)(x² - 2x + 4)

Front

What is the first step in factoring a sum or difference of cubes?

Back

Identify a and b such that a³ or b³ corresponds to the terms.

Front

Factor: 64x³ - 1

Back

(4x - 1)(16x² + 4x + 1)

Front

What is the significance of the coefficients in the sum/difference of cubes formula?

Back

They determine the structure of the quadratic factor.

Front

Factor the sum of cubes: 27 + x³

Back

(x + 3)(x² - 3x + 9)