## 17Calculus Precalculus - Factoring Cubic Polynomials

##### 17Calculus

Sum And Difference of Cubic Polynomials

Factoring two terms, both of them cubes does not come up very often in calculus. But you will see it. We include this discussion to give you a place to come back to when you need to remind yourself how to factor these types of equations.

$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$

$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$

For a discussion and some good examples of the sum and difference of cubes, go to this Purple Math page .

Okay, try these practice problems.

### Practice

Unless otherwise instructed, factor these cubic polynomials, giving your answers in exact form.

$$x^3 - 27$$

Problem Statement

Factor $$x^3 - 27$$

Solution

### 2666 video solution

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$$8x^3 - 64$$

Problem Statement

Factor $$8x^3 - 64$$

Solution

### 2667 video solution

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$$8-t^3$$

Problem Statement

Factor $$8-t^3$$

Solution

### 2668 video solution

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$$125A^3 + 27B^3$$

Problem Statement

Factor $$125A^3 + 27B^3$$

Solution

### 2669 video solution

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$$64x^3 + 125$$

Problem Statement

Factor the polynomial $$64x^3 + 125$$

Solution

### 2670 video solution

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$$27y^3 - 8$$

Problem Statement

Factor $$27y^3 - 8$$

Solution

### 2671 video solution

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$$8x^3 + 27$$

Problem Statement

Factor $$8x^3 + 27$$

Solution

### 2672 video solution

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$$27x^3 + 64y^3$$

Problem Statement

Factor $$27x^3 + 64y^3$$

Solution

### 2673 video solution

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$$64y^3 - 125$$

Problem Statement

Factor $$64y^3 - 125$$

Solution

### 2674 video solution

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$$8y^3-27$$

Problem Statement

Factor the polynomial $$8y^3-27$$

Solution

### 2675 video solution

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$$x^6 - 64y^9$$

Problem Statement

Factor $$x^6 - 64y^9$$

$$(x^2-4y^3)(x^4+4x^2y^3+16y^6)$$

Problem Statement

Factor $$x^6 - 64y^9$$

Solution

### 2676 video solution

$$(x^2-4y^3)(x^4+4x^2y^3+16y^6)$$

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$$(2x+3y)^3 - 343$$

Problem Statement

Factor the polynomial $$(2x+3y)^3 - 343$$

Solution

Not all instructors require students to multiply out the larger term. Check with your instructor to see what they expect.

### 2677 video solution

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