Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x3−3x2+3x−28
Evaluate
(x−1)3−27
Expand the expression
x3−3x2+3x−1−27
Solution
x3−3x2+3x−28
Show Solution
Factor the expression
(x−4)(x2+x+7)
Evaluate
(x−1)3−27
Rewrite the expression in exponential form
(x−1)3−33
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(x−1−3)((x−1)2+(x−1)×3+32)
Evaluate
(x−1−3)((x−1)2+3(x−1)+32)
Evaluate
(x−1−3)((x−1)2+3(x−1)+9)
Calculate
(x−4)((x−1)2+3(x−1)+9)
Solution
More Steps
Simplify
(x−1)2+3(x−1)+9
Simplify
More Steps
Simplify
3(x−1)
Apply the distributive property
3x+3(−1)
Multiply the terms
3x−3
(x−1)2+3x−3+9
Simplify
(x−1)2+3x+6
Expand the expression
x2−2x+1+3x+6
Add the terms
More Steps
Evaluate
−2x+3x
Collect like terms by calculating the sum or difference of their coefficients
(−2+3)x
Add the numbers
x
x2+x+1+6
Add the numbers
x2+x+7
(x−4)(x2+x+7)
Show Solution
Find the roots
x=4
Evaluate
(x−1)3−27
To find the roots of the expression,set the expression equal to 0
(x−1)3−27=0
Move the constant to the right-hand side and change its sign
(x−1)3=0+27
Removing 0 doesn't change the value,so remove it from the expression
(x−1)3=27
Take the 3-th root on both sides of the equation
3(x−1)3=327
Calculate
x−1=327
Evaluate the root
More Steps
Evaluate
327
Write the number in exponential form with the base of 3
333
Reduce the index of the radical and exponent with 3
3
x−1=3
Move the constant to the right-hand side and change its sign
x=3+1
Solution
x=4
Show Solution