Sum and Difference of Cubes

Front

What is the formula for the sum of cubes?

Back

a³ + b³ = (a + b)(a² - ab + b²)

Front

What is the formula for the difference of cubes?

Back

a³ - b³ = (a - b)(a² + ab + b²)

Front

How do you identify a sum or difference of cubes?

Back

Look for expressions in the form a³ ± b³, where a and b are real numbers.

Front

Can the expression 3x³ + 24 be factored as a sum of cubes?

Back

Yes, getting GCF first.

Front

Factor the expression x³ + 1.

Back

(x + 1)(x² - x + 1)

Front

Factor the expression 8x³ - 1.

Back

(2x - 1)(4x² + 2x + 1)

Front

Factor the expression 27x³ - 64.

Back

(3x - 4)(9x² + 12x + 16)

Front

Factor the sum of cubes 2x³ + 128.

Back

2(x + 4)(x² - 4x + 16)

Front

What is the first step in factoring a sum or difference of cubes?

Back

Identify the GCF (Greatest Common Factor) if applicable.

Front

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

Back

They affect the values of a and b in the formulas.