sum/difference of cubes

Front

What is the formula for the sum of cubes?

Back

The formula for the sum of cubes is: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

What is the formula for the difference of cubes?

Back

The formula for the difference of cubes is: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

Factor the expression: 27x³ - 64

Back

(3x - 4)(9x² + 12x + 16).

Front

Solve the equation: 8x³ - 1 = 0

Back

x = \frac{1}{2}; x = -\frac{1}{4} \pm 0.433i.

Front

Factor the expression: 216x³ + 125

Back

(6x + 5)(36x² - 30x + 25).

Front

Identify the expression that is a difference of cubes: 8x³ - 27

Back

8x³ - 27 is a difference of cubes because it can be expressed as (2x)³ - 3³.

Front

What is a cube?

Back

A cube is a number raised to the third power, represented as a^3.

Front

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

Back

The coefficients in the formulas help in determining the factors of the cubic expressions.

Front

Factor the expression: x³ - 27

Back

(x - 3)(x² + 3x + 9).

Front

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

Back

Identify the two cubes and apply the difference of cubes formula.