Textbook Question
In Exercises 49–64, factor any perfect square trinomials, or state that the polynomial is prime.64y² − 16y + 1
894
views
0. Review of Algebra
Factoring Polynomials
3:06 minutesProblem 58
Textbook Question
Factor using the formula for the sum or difference of two cubes.
Verified step by step guidance1
Recognize that the expression \(x^3 + 64\) is a sum of two cubes because \$64\( can be written as \)4^3$.
Recall the formula for the sum of two cubes: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\).
Identify \(a = x\) and \(b = 4\) in the expression \(x^3 + 4^3\).
Apply the sum of cubes formula: \((x + 4)(x^2 - 4x + 16)\).
Write the fully factored form as \((x + 4)(x^2 - 4x + 16)\).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sum of Cubes Formula
The sum of cubes formula is used to factor expressions of the form a^3 + b^3. It states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). This formula helps break down cubic expressions into simpler polynomial factors.
Recommended video:
Guided course
03:41
Special Products - Cube Formulas
Identifying Perfect Cubes
To apply the sum or difference of cubes formula, recognize each term as a perfect cube. For example, x^3 is the cube of x, and 64 is the cube of 4 since 4^3 = 64. Correct identification is essential for accurate factoring.
Recommended video:
Guided course
03:41Special Products - Cube Formulas
Factoring Polynomials
Factoring polynomials involves rewriting them as products of simpler polynomials. Using special formulas like the sum or difference of cubes simplifies complex expressions, making it easier to solve equations or analyze functions.
Recommended video:
Guided course
07:30Introduction to Factoring Polynomials
Related Videos
Related Practice