Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
(x2−1)14
Evaluate
(x2−1)2(x2−1)4(x2−1)8
Multiply the terms with the same base by adding their exponents
(x2−1)2+4+8
Solution
(x2−1)14
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Factor the expression
(x−1)14(x+1)14
Evaluate
(x2−1)2(x2−1)4(x2−1)8
Multiply the terms with the same base by adding their exponents
(x2−1)2+4+8
Add the numbers
(x2−1)14
Use a2−b2=(a−b)(a+b) to factor the expression
((x−1)(x+1))14
Solution
(x−1)14(x+1)14
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Find the roots
x1=−1,x2=1
Evaluate
(x2−1)2(x2−1)4(x2−1)8
To find the roots of the expression,set the expression equal to 0
(x2−1)2(x2−1)4(x2−1)8=0
Multiply
More Steps
Multiply the terms
(x2−1)2(x2−1)4(x2−1)8
Multiply the terms with the same base by adding their exponents
(x2−1)2+4+8
Add the numbers
(x2−1)14
(x2−1)14=0
The only way a power can be 0 is when the base equals 0
x2−1=0
Move the constant to the right-hand side and change its sign
x2=0+1
Removing 0 doesn't change the value,so remove it from the expression
x2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
Solution
x1=−1,x2=1
Show Solution