Sum and Difference of Two Squares

Front

What is the formula for the difference of squares?

Back

The formula for the difference of squares is: a² - b² = (a - b)(a + b).

Front

What is the formula for the sum of cubes?

Back

The formula for the sum of cubes is: a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the formula for the difference of cubes?

Back

The formula for the difference of cubes is: a³ - b³ = (a - b)(a² + ab + b²).

Front

How do you factor the expression 8x³ - 27?

Back

8x³ - 27 can be factored as (2x - 3)(4x² + 6x + 9).

Front

What is the first step in factoring 3x³ + 24?

Back

The first step is to factor out the greatest common factor (GCF), which is 3. This gives 3(x³ + 8).

Front

Can the expression x² - 16 be factored? If so, how?

Back

Yes, x² - 16 can be factored as (x - 4)(x + 4) using the difference of squares formula.

Front

What is the GCF of the expression 3x³ + 24?

Back

The GCF of 3x³ + 24 is 3.

Front

What is the result of factoring the expression 2x³ - 18?

Back

The expression can be factored as 2(x³ - 9) = 2(x - 3)(x² + 3x + 9).

Front

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

Back

A sum of squares (a² + b²) cannot be factored over the real numbers, while a difference of squares (a² - b²) can be factored as (a - b)(a + b).

Front

What is the result of factoring the expression x³ + 27?

Back

The expression can be factored as (x + 3)(x² - 3x + 9).