11-14 Difference of Squares / Cubes

Front

What is the formula for the difference of cubes?

Back

a³ - b³ = (a - b)(a² + ab + b²)

Front

What is the formula for the difference of squares?

Back

a² - b² = (a - b)(a + b)

Front

What does it mean for an expression to be a sum of squares?

Back

An expression that cannot be factored into real numbers, e.g., a² + b².

Front

Factor the expression: 49x² + 16.

Back

does not factor (SUM of squares)

Front

Factor the expression: 4y² - 9.

Back

(2y + 3)(2y - 3)

Front

Factor the expression: x² - 16.

Back

(x + 4)(x - 4)

Front

What is the result of factoring 8x³ - 27?

Back

(2x - 3)(4x² + 6x + 9)

Front

What is the difference between a sum of squares and a difference of squares?

Back

A sum of squares cannot be factored over the reals, while a difference of squares can.

Front

What is the first step in factoring a difference of squares?

Back

Identify the two perfect squares and apply the formula a² - b² = (a - b)(a + b).

Front

What is the significance of the coefficients in the difference of cubes formula?

Back

They determine the specific values of a and b in the expression a³ - b³.