Sum and Difference of Cubes

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 expression: 8x^3 - 1

Back

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

Front

Factor the expression: 27x^3 + 8

Back

(3x + 2)(9x^2 - 6x + 4)

Front

What is the result of factoring 64 - 27a^3?

Back

(4 - 3a)(9a^2 + 12a + 16)

Front

How do you factor the expression 2x^3 + 128?

Back

2(x + 4)(x^2 - 4x + 16)

Front

What is the factored form of x^3 + 1?

Back

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

Front

What is the significance of the coefficients in the sum and difference of cubes?

Back

The coefficients can affect the factors and the resulting quadratic expressions.

Front

How can you identify a sum or difference of cubes in an expression?

Back

Look for terms that are perfect cubes, such as a^3 and b^3.

Front

What is a perfect cube?

Back

A number that can be expressed as the cube of an integer, e.g., 1, 8, 27, 64.