Factoring Special Cases

Front

Define the difference of cubes.

Back

The difference of cubes is a special case of factoring that applies to expressions of the form a^3 - b^3, which can be factored as (a - b)(a^2 + ab + b^2).

Front

Factor the expression: 64 - 27a^3.

Back

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

Front

Define the sum of cubes.

Back

The sum of cubes is a special case of factoring that applies to expressions of the form a^3 + b^3, which can be factored as (a + b)(a^2 - ab + b^2).

Front

Factor the expression: 343m^3 + 8.

Back

(7m + 2)(49m^2 - 14m + 4) (using the sum of cubes formula)

Front

What is the formula for factoring a^3 - b^3?

Back

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

Front

Factor the expression: 27x^3 + 8.

Back

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

Front

What is the formula for factoring a^3 + b^3?

Back

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

Front

Factor the expression: 125x^3 - 64.

Back

(5x - 4)(25x^2 + 20x + 16)

Front

What is the first step in factoring a polynomial expression?

Back

Identify if the expression is a special case (like difference or sum of cubes) or if it can be factored by grouping.

Front

Explain the significance of the coefficients in the factored form of a polynomial.

Back

The coefficients in the factored form provide information about the roots of the polynomial and can help in graphing the function.