MHB Is this the simplified form of (a + b)^3 - 8c^3?

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Difference
Click For Summary
The discussion focuses on factoring the expression (a + b)^3 - 8c^3 as a difference of cubes. Participants confirm that the expression can be rewritten as (a + b)^3 - (2c)^3. The difference of cubes formula is applied, leading to the factorization (a + b - 2c)((a + b)^2 + 2c(a + b) + 4c^2). Clarifications are made regarding the interpretation of -8c^3, emphasizing that it can be expressed as -(2c)^3. The conversation concludes with a consensus on the correct application of the difference of cubes formula.
mathdad
Messages
1,280
Reaction score
0
Factor (a + b)^3 - 8c^3.

Is this the difference of cubes?

Formula:

x^3 - a^3 = (x - a)(x^2 + ax + a^2)

Let x = (a + b)

Let a = 8

(a + b - 8)((a + b)^2 + 8(a + b) + 64)

Correct?
 
Mathematics news on Phys.org
I would begin by writing the expression as the difference of cubes:

$$(a+b)^3-8c^3=(a+b)^3-(2c)^3$$

Now apply the difference of cubes formula...:D
 
Why did you write -8c^3 as -(2c)^3?

The number 8 is not part of c^3.

Are you saying that -8•c^3 = (-8c)^3?
 
RTCNTC said:
Why did you write -8c^3 as -(2c)^3?

The number 8 is not part of c^3.

Are you saying that -8•c^3 = (-8c)^3?

I applied the exponential property:

$$x^ny^n=(xy)^n$$

Since $8=2^3$, we can write:

$$8c^3=2^3c^3=(2c)^3$$
 
I got it now.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB How do you factor (p)^3 - 8c^3 when p = (a + b) and b = 2c?
  • · Replies 3 ·
Replies
3
Views
1K
MHB Min Value of $\dfrac{a+3c}{a+2b+c}$+$\dfrac{4b}{a+b+2c}$+$\dfrac{8c}{a+b+3c}$
  • · Replies 1 ·
Replies
1
Views
2K
High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
MHB Evaluate the constant in polynomial function
  • · Replies 7 ·
Replies
7
Views
1K
MHB Is the Calculation of $(3 \diamond 8) \square 2 = 1940$ Correct?
  • · Replies 2 ·
Replies
2
Views
974
MHB V.02.Binary operator by a*b=a+8b
  • · Replies 2 ·
Replies
2
Views
803
MHB Factoring Fractional Expression
  • · Replies 4 ·
Replies
4
Views
2K
MHB -c5.LCM and Prime Factorization of A,B,C
  • · Replies 3 ·
Replies
3
Views
1K
High School Fractional/decimal powers
  • · Replies 10 ·
Replies
10
Views
2K
MHB Real Roots of Cubic Equation: $x^3+a^3x^2+b^3x+c^3=0$
  • · Replies 1 ·
Replies
1
Views
2K