Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x6−26x3+25
Evaluate
(x3−1)(x3−25)
Apply the distributive property
x3×x3−x3×25−x3−(−25)
Multiply the terms
More Steps
Evaluate
x3×x3
Use the product rule an×am=an+m to simplify the expression
x3+3
Add the numbers
x6
x6−x3×25−x3−(−25)
Use the commutative property to reorder the terms
x6−25x3−x3−(−25)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x6−25x3−x3+25
Solution
More Steps
Evaluate
−25x3−x3
Collect like terms by calculating the sum or difference of their coefficients
(−25−1)x3
Subtract the numbers
−26x3
x6−26x3+25
Show Solution
Factor the expression
(x−1)(x2+x+1)(x3−25)
Evaluate
(x3−1)(x3−25)
Solution
More Steps
Evaluate
x3−1
Calculate
x3+x2+x−x2−x−1
Rewrite the expression
x×x2+x×x+x−x2−x−1
Factor out x from the expression
x(x2+x+1)−x2−x−1
Factor out −1 from the expression
x(x2+x+1)−(x2+x+1)
Factor out x2+x+1 from the expression
(x−1)(x2+x+1)
(x−1)(x2+x+1)(x3−25)
Show Solution
Find the roots
x1=1,x2=325
Alternative Form
x1=1,x2≈2.924018
Evaluate
(x3−1)(x3−25)
To find the roots of the expression,set the expression equal to 0
(x3−1)(x3−25)=0
Separate the equation into 2 possible cases
x3−1=0x3−25=0
Solve the equation
More Steps
Evaluate
x3−1=0
Move the constant to the right-hand side and change its sign
x3=0+1
Removing 0 doesn't change the value,so remove it from the expression
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
x=1x3−25=0
Solve the equation
More Steps
Evaluate
x3−25=0
Move the constant to the right-hand side and change its sign
x3=0+25
Removing 0 doesn't change the value,so remove it from the expression
x3=25
Take the 3-th root on both sides of the equation
3x3=325
Calculate
x=325
x=1x=325
Solution
x1=1,x2=325
Alternative Form
x1=1,x2≈2.924018
Show Solution