Sum/Difference of Cubes and Grouping

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

Factor the expression: x³ + 27

Back

(x + 3)(x² - 3x + 9)

Front

Factor the expression: x³ - 8

Back

(x - 2)(x² + 2x + 4)

Front

Factor by grouping: 2x³ - 8x² - x + 4

Back

(2x² - 1)(x - 4)

Front

Factor by grouping: 10x³ + 5x² - 6x - 3

Back

(5x² - 3)(2x + 1)

Front

What is the first step in factoring by grouping?

Back

Group the terms into pairs and factor out the common factor from each pair.

Front

What does it mean for an expression to be prime in the context of factoring?

Back

An expression is prime if it cannot be factored into simpler polynomial expressions.

Front

How do you identify a sum of cubes?

Back

A sum of cubes is 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 is in the form a³ - b³, where both a and b are perfect cubes.