Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2x3+24x
Evaluate
(x+2)3+(x−2)3
Expand the expression
x3+6x2+12x+8+(x−2)3
Expand the expression
x3+6x2+12x+8+x3−6x2+12x−8
Add the terms
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Evaluate
x3+x3
Collect like terms by calculating the sum or difference of their coefficients
(1+1)x3
Add the numbers
2x3
2x3+6x2+12x+8−6x2+12x−8
The sum of two opposites equals 0
More Steps
Evaluate
6x2−6x2
Collect like terms
(6−6)x2
Add the coefficients
0×x2
Calculate
0
2x3+0+12x+8+12x−8
Remove 0
2x3+12x+8+12x−8
Add the terms
More Steps
Evaluate
12x+12x
Collect like terms by calculating the sum or difference of their coefficients
(12+12)x
Add the numbers
24x
2x3+24x+8−8
Solution
2x3+24x
Show Solution
Factor the expression
2x(x2+12)
Evaluate
(x+2)3+(x−2)3
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(x+2+x−2)((x+2)2−(x+2)(x−2)+(x−2)2)
Evaluate
(x+2+x−2)((x+2)2+(−x−2)(x−2)+(x−2)2)
Calculate
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Simplify
x+2+x−2
Add the terms
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Evaluate
x+x
Collect like terms by calculating the sum or difference of their coefficients
(1+1)x
Add the numbers
2x
2x+2−2
Since two opposites add up to 0,remove them form the expression
2x
2x((x+2)2+(−x−2)(x−2)+(x−2)2)
Solution
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Simplify
(x+2)2+(−x−2)(x−2)+(x−2)2
Simplify
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Simplify
(−x−2)(x−2)
Apply the distributive property
−x×x−x(−2)−2x−2(−2)
Multiply the terms
−x2−x(−2)−2x−2(−2)
Use the commutative property to reorder the terms
−x2+2x−2x−2(−2)
Multiply the terms
−x2+2x−2x+4
(x+2)2−x2+2x−2x+4+(x−2)2
The sum of two opposites equals 0
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Evaluate
2x−2x
Collect like terms
(2−2)x
Add the coefficients
0×x
Calculate
0
(x+2)2−x2+0+4+(x−2)2
Remove 0
(x+2)2−x2+4+(x−2)2
Expand the expression
x2+4x+4−x2+4+(x−2)2
Expand the expression
x2+4x+4−x2+4+x2−4x+4
Calculate the sum or difference
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Evaluate
x2−x2+x2
Collect like terms by calculating the sum or difference of their coefficients
(1−1+1)x2
Calculate the sum or difference
x2
x2+4x+4+4−4x+4
The sum of two opposites equals 0
More Steps
Evaluate
4x−4x
Collect like terms
(4−4)x
Add the coefficients
0×x
Calculate
0
x2+0+4+4+4
Remove 0
x2+4+4+4
Add the numbers
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Evaluate
4+4+4
Add the numbers
8+4
Add the numbers
12
x2+12
2x(x2+12)
Show Solution
Find the roots
x1=−23×i,x2=23×i,x3=0
Alternative Form
x1≈−3.464102i,x2≈3.464102i,x3=0
Evaluate
(x+2)3+(x−2)3
To find the roots of the expression,set the expression equal to 0
(x+2)3+(x−2)3=0
Factor the expression
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Evaluate
(x+2)3+(x−2)3
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(x+2+x−2)((x+2)2−(x+2)(x−2)+(x−2)2)
Evaluate
(x+2+x−2)((x+2)2+(−x−2)(x−2)+(x−2)2)
(x+2+x−2)((x+2)2+(−x−2)(x−2)+(x−2)2)=0
Separate the equation into 2 possible cases
x+2+x−2=0(x+2)2+(−x−2)(x−2)+(x−2)2=0
Solve the equation
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Evaluate
x+2+x−2=0
Calculate the sum or difference
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Evaluate
x+2+x−2
Add the terms
2x+2−2
Since two opposites add up to 0,remove them form the expression
2x
2x=0
Rewrite the expression
x=0
x=0(x+2)2+(−x−2)(x−2)+(x−2)2=0
Solve the equation
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Evaluate
(x+2)2+(−x−2)(x−2)+(x−2)2=0
Calculate
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Evaluate
(x+2)2+(−x−2)(x−2)+(x−2)2
Expand the expression
x2+4x+4+(−x−2)(x−2)+(x−2)2
Expand the expression
x2+4x+4+4−x2+(x−2)2
Expand the expression
x2+4x+4+4−x2+x2−4x+4
Calculate the sum or difference
x2+4x+4+4−4x+4
The sum of two opposites equals 0
x2+0+4+4+4
Remove 0
x2+4+4+4
Add the numbers
x2+12
x2+12=0
Move the constant to the right-hand side and change its sign
x2=0−12
Removing 0 doesn't change the value,so remove it from the expression
x2=−12
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−12
Simplify the expression
More Steps
Evaluate
−12
Evaluate the power
12×−1
Evaluate the power
12×i
Evaluate the power
23×i
x=±(23×i)
Separate the equation into 2 possible cases
x=23×ix=−23×i
x=0x=23×ix=−23×i
Solution
x1=−23×i,x2=23×i,x3=0
Alternative Form
x1≈−3.464102i,x2≈3.464102i,x3=0
Show Solution