Sum/Difference of Cubes and Grouping

Front

What is the formula for factoring the difference of cubes?

Back

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Front

What is the formula for factoring the sum of cubes?

Back

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Front

Factor the difference of cubes: x^3 - 125

Back

(x - 5)(x^2 + 5x + 25)

Front

Factor the sum of cubes: x^3 + 27

Back

(x + 3)(x^2 - 3x + 9)

Front

Factor the expression: 8x^3 - 1

Back

(2x - 1)(4x^2 + 2x + 1)

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

Which number is both a perfect square and a perfect cube?

Back

64 (since 8^2 = 64 and 4^3 = 64)

Front

Factor by grouping: 20x^3 - 25x^2 + 4x - 5

Back

(5x^2 + 1)(4x - 5)

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.