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 16n² - 9?

Back

You can factor 16n² - 9 using the difference of squares: 16n² - 9 = (4n - 3)(4n + 3).

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: 3(x³ + 8).

Front

What is the GCF of -6n² + 42n?

Back

The GCF is -6n, so you can factor it out: -6n(n - 7).

Front

What type of expression is 8x³ - 27?

Back

8x³ - 27 is a difference of cubes, which can be factored as (2x - 3)(4x² + 6x + 9).

Front

What is the result of factoring the expression x² - 16?

Back

The result is (x - 4)(x + 4), using the difference of squares formula.

Front

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

Back

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

Front

What is the significance of recognizing GCF in factoring?

Back

Recognizing the GCF simplifies the expression and makes it easier to factor further.