Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x7−1
Evaluate
x4×x3−1
Solution
More Steps
Evaluate
x4×x3
Use the product rule an×am=an+m to simplify the expression
x4+3
Add the numbers
x7
x7−1
Show Solution
Factor the expression
(x−1)(x6+x5+x4+x3+x2+x+1)
Evaluate
x4×x3−1
Multiply the terms
More Steps
Evaluate
x4×x3
Use the product rule an×am=an+m to simplify the expression
x4+3
Add the numbers
x7
x7−1
Calculate
x7+x6+x5+x4+x3+x2+x−x6−x5−x4−x3−x2−x−1
Rewrite the expression
x×x6+x×x5+x×x4+x×x3+x×x2+x×x+x−x6−x5−x4−x3−x2−x−1
Factor out x from the expression
x(x6+x5+x4+x3+x2+x+1)−x6−x5−x4−x3−x2−x−1
Factor out −1 from the expression
x(x6+x5+x4+x3+x2+x+1)−(x6+x5+x4+x3+x2+x+1)
Solution
(x−1)(x6+x5+x4+x3+x2+x+1)
Show Solution
Find the roots
x=1
Evaluate
x4×x3−1
To find the roots of the expression,set the expression equal to 0
x4×x3−1=0
Multiply the terms
More Steps
Evaluate
x4×x3
Use the product rule an×am=an+m to simplify the expression
x4+3
Add the numbers
x7
x7−1=0
Move the constant to the right-hand side and change its sign
x7=0+1
Removing 0 doesn't change the value,so remove it from the expression
x7=1
Take the 7-th root on both sides of the equation
7x7=71
Calculate
x=71
Solution
x=1
Show Solution