Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
11z4−22z5−4+8z
Evaluate
11z3×z(1−2z)−4(1−2z)
Multiply
More Steps
Multiply the terms
11z3×z(1−2z)
Multiply the terms with the same base by adding their exponents
11z3+1(1−2z)
Add the numbers
11z4(1−2z)
11z4(1−2z)−4(1−2z)
Expand the expression
More Steps
Calculate
11z4(1−2z)
Apply the distributive property
11z4×1−11z4×2z
Any expression multiplied by 1 remains the same
11z4−11z4×2z
Multiply the terms
More Steps
Evaluate
11z4×2z
Multiply the numbers
22z4×z
Multiply the terms
22z5
11z4−22z5
11z4−22z5−4(1−2z)
Solution
More Steps
Calculate
−4(1−2z)
Apply the distributive property
−4×1−(−4×2z)
Any expression multiplied by 1 remains the same
−4−(−4×2z)
Multiply the numbers
−4−(−8z)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4+8z
11z4−22z5−4+8z
Show Solution
Factor the expression
(11z4−4)(1−2z)
Evaluate
11z3×z(1−2z)−4(1−2z)
Multiply
More Steps
Evaluate
11z3×z(1−2z)
Multiply the terms with the same base by adding their exponents
11z3+1(1−2z)
Add the numbers
11z4(1−2z)
11z4(1−2z)−4(1−2z)
Solution
(11z4−4)(1−2z)
Show Solution
Find the roots
z1=−1145324,z2=21,z3=1145324
Alternative Form
z1≈−0.776545,z2=0.5,z3≈0.776545
Evaluate
11z3×z(1−2z)−4(1−2z)
To find the roots of the expression,set the expression equal to 0
11z3×z(1−2z)−4(1−2z)=0
Multiply
More Steps
Multiply the terms
11z3×z(1−2z)
Multiply the terms with the same base by adding their exponents
11z3+1(1−2z)
Add the numbers
11z4(1−2z)
11z4(1−2z)−4(1−2z)=0
Calculate
More Steps
Evaluate
11z4(1−2z)−4(1−2z)
Expand the expression
More Steps
Calculate
11z4(1−2z)
Apply the distributive property
11z4×1−11z4×2z
Any expression multiplied by 1 remains the same
11z4−11z4×2z
Multiply the terms
11z4−22z5
11z4−22z5−4(1−2z)
Expand the expression
More Steps
Calculate
−4(1−2z)
Apply the distributive property
−4×1−(−4×2z)
Any expression multiplied by 1 remains the same
−4−(−4×2z)
Multiply the numbers
−4−(−8z)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4+8z
11z4−22z5−4+8z
11z4−22z5−4+8z=0
Factor the expression
(−2z+1)(11z4−4)=0
Separate the equation into 2 possible cases
−2z+1=011z4−4=0
Solve the equation
More Steps
Evaluate
−2z+1=0
Move the constant to the right-hand side and change its sign
−2z=0−1
Removing 0 doesn't change the value,so remove it from the expression
−2z=−1
Change the signs on both sides of the equation
2z=1
Divide both sides
22z=21
Divide the numbers
z=21
z=2111z4−4=0
Solve the equation
More Steps
Evaluate
11z4−4=0
Move the constant to the right-hand side and change its sign
11z4=0+4
Removing 0 doesn't change the value,so remove it from the expression
11z4=4
Divide both sides
1111z4=114
Divide the numbers
z4=114
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±4114
Simplify the expression
More Steps
Evaluate
4114
To take a root of a fraction,take the root of the numerator and denominator separately
41144
Simplify the radical expression
4112
Multiply by the Conjugate
411×41132×4113
Simplify
411×41132×41331
Multiply the numbers
411×411345324
Multiply the numbers
1145324
z=±1145324
Separate the equation into 2 possible cases
z=1145324z=−1145324
z=21z=1145324z=−1145324
Solution
z1=−1145324,z2=21,z3=1145324
Alternative Form
z1≈−0.776545,z2=0.5,z3≈0.776545
Show Solution