Table of Contents

- 1 What is the factor of 27x 3 8?
- 2 What is the factored form of 27x 3 64?
- 3 Can 9×2 − 24x 16 be factored using the perfect square trinomial?
- 4 How do you factor 1000?
- 5 How do you factor the difference of two cubes?
- 6 What is the sum of cubes?
- 7 How is the sum of 2 7 x 3 + 8 factored?
- 8 How does the factoring calculator work in the editor?
- 9 What are the factor pairs for the number 18?

## What is the factor of 27x 3 8?

For example, the factored form of 27×3 – 8 (a = 3x, b = 2) is (3x – 2)(9×2 + 6x + 4).

## What is the factored form of 27x 3 64?

Answer: The factored form of x3 – 64 is (x – 4)(x2 + 4x + 16). The factored form of 27×3 – 8y3 is (3x – 2y)(9×2 + 6xy + 4y2). Notice that the basic construction of the factorization is the same as it is for the sum of cubes; the difference is in the + and – signs.

**How do you factor 8x 3 y 3?**

Algebra Examples Rewrite 8×3 8 x 3 as (2x)3 ( 2 x ) 3 . Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2) a 3 – b 3 = ( a – b ) ( a 2 + a b + b 2 ) where a=2x a = 2 x and b=y . Simplify. Apply the product rule to 2x 2 x .

### Can 9×2 − 24x 16 be factored using the perfect square trinomial?

Here 9 can be written as (−3)2, so the middle term is 2(−3)x = −6x. So when the sign of the middle term is negative, the trinomial may be factored as (a – b)2. In this case, the middle term is 2(3x)( −4) = −24x. So the trinomial 9×2 – 24x + 16 is a perfect square and factors as (3x – 4)2.

### How do you factor 1000?

Factors of 1000: 1 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500,and 1000. Prime Factorization of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5.

**What are the factors of 64×3 1?**

Algebra Examples Rewrite 64×3 64 x 3 as (4x)3 ( 4 x ) 3 . Rewrite 1 as 13 . Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2) a 3 – b 3 = ( a – b ) ( a 2 + a b + b 2 ) where a=4x a = 4 x and b=1 .

#### How do you factor the difference of two cubes?

The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3+y3=(x+y)(x2−xy+y2) and x3−y3=(x−y)(x2+xy+y2) .

#### What is the sum of cubes?

Sum or Difference of Cubes A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the form a 3 – b 3 is called a difference of cubes.

**What is the completely factored form of 9×2 24x 16?**

The completely factored form of 9×2 + 24x + 16 is(3x + 4)(3x + 4).

## How is the sum of 2 7 x 3 + 8 factored?

Rewrite 2 7 x 3 + 8 as ( 3 x) 3 + 2 3. The sum of cubes can be factored using the rule: a 3 + b 3 = ( a + b) ( a 2 − a b + b 2). Polynomial 9 x 2 − 6 x + 4 is not factored since it does not have any rational roots.

## How does the factoring calculator work in the editor?

Factoring Calculator. Enter the expression you want to factor in the editor. The Factoring Calculator transforms complex expressions into a product of simpler factors. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions.

**Which is a perfect cube 27×3 or 8?**

Before we start, notice this: 27×3 and 8 are both perfect cubes of 3x and 2 respectively.

### What are the factor pairs for the number 18?

Testing the integer values 1 through 4 for division into 18 with a 0 remainder we get these factor pairs: (1 and 18), (2 and 9), (3 and 6). The factors of 18 are 1, 2, 3, 6, 9, 18. All of the above information and methods generally apply to factoring negative numbers.