Factor sums and differences of cubes

Learning Objectives Identify binomials that are sums or differences of perfect cubes. Recall and correctly write the formulas for factoring a³ + b³ and a³ - b³. Apply the formulas to factor binomials involving integers and single variables. Factor more complex expressions involving coefficients and variables with exponents that are multiples of three. Recognize that the resulting trinomial factor from the sum or difference of cubes formula is prime over the real numbers. Solve polynomial equations by first factoring a sum or difference of cubes. Ever seen a complex polynomial like x³ + 512 and wondered if there's a secret pattern to break it down? 🤔 There is, and it's an elegant one! This tutorial will teach you two powerful formulas for factoring binomials that...

TermDefinitionExample Perfect CubeA number or expression that is the result of multiplying a number or expression by itself three times.27 is a perfect cube because 3 × 3 × 3 = 3³. Also, 64y⁶ is a perfect cube because (4y²)³ = 64y⁶. Cube RootThe base number or expression that is multiplied by itself three times to get the perfect cube.The cube root of 125 is 5, written as ³√125 = 5. BinomialA polynomial expression with exactly two terms, separated by a plus or minus sign.x³ - 8 TrinomialA polynomial expression with exactly three terms.x² + 2x + 4 FactoringThe process of breaking down a polynomial into a product of its factors (simpler polynomials).Factoring x² - 9 gives (x - 3)(x + 3). Prime PolynomialA polynomial with integer coefficients that cannot be factored into polynomials of a low...

Sum of Cubes Formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) Use this formula when you have two perfect cubes added together. Identify the cube root of the first term as 'a' and the cube root of the second term as 'b', then substitute them into the formula. Difference of Cubes Formula a^3 - b^3 = (a - b)(a^2 + ab + b^2) Use this formula when you have two perfect cubes with a subtraction sign between them. Identify 'a' and 'b' in the same way and substitute into this pattern.