Factoring Cubes

Front

What is the formula for factoring a sum of cubes?

Back

The formula for factoring a sum of cubes a³ + b³ is (a + b)(a² - ab + b²).

Front

What is the formula for factoring a difference of cubes?

Back

The formula for factoring a difference of cubes a³ - b³ is (a - b)(a² + ab + b²).

Front

Factor the expression: x³ + 125

Back

(x + 5)(x² - 5x + 25)

Front

Factor the expression: 8x³ + 27y³

Back

(2x + 3y)(4x² - 6xy + 9y²)

Front

Factor the expression: w³ + 343c³

Back

(w + 7c)(w² - 7wc + 49c²)

Front

Factor the expression: 343m³ - 64n³

Back

(7m - 4n)(49m² + 28mn + 16n²)

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all terms.

Front

How do you identify a sum of cubes?

Back

A sum of cubes can be identified if it can be expressed in the form a³ + b³, where both a and b are perfect cubes.

Front

How do you identify a difference of cubes?

Back

A difference of cubes can be identified if it can be expressed in the form a³ - b³, where both a and b are perfect cubes.

Front

What is a perfect cube?

Back

A perfect cube is a number that can be expressed as the cube of an integer, such as 1, 8, 27, 64, etc.