Question
Simplify the expression
z7−4z11
Evaluate
z5(z2−4z6)
Apply the distributive property
z5×z2−z5×4z6
Multiply the terms
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Evaluate
z5×z2
Use the product rule an×am=an+m to simplify the expression
z5+2
Add the numbers
z7
z7−z5×4z6
Solution
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Evaluate
z5×4z6
Use the commutative property to reorder the terms
4z5×z6
Multiply the terms
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Evaluate
z5×z6
Use the product rule an×am=an+m to simplify the expression
z5+6
Add the numbers
z11
4z11
z7−4z11
Show Solution
Factor the expression
z7(1−2z2)(1+2z2)
Evaluate
z5(z2−4z6)
Factor the expression
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Evaluate
z2−4z6
Rewrite the expression
z2−z2×4z4
Factor out z2 from the expression
z2(1−4z4)
Use a2−b2=(a−b)(a+b) to factor the expression
z2(1−2z2)(1+2z2)
z5×z2(1−2z2)(1+2z2)
Solution
z7(1−2z2)(1+2z2)
Show Solution
Find the roots
z1=−22,z2=0,z3=22
Alternative Form
z1≈−0.707107,z2=0,z3≈0.707107
Evaluate
(z5)(z2−4z6)
To find the roots of the expression,set the expression equal to 0
(z5)(z2−4z6)=0
Calculate
z5(z2−4z6)=0
Separate the equation into 2 possible cases
z5=0z2−4z6=0
The only way a power can be 0 is when the base equals 0
z=0z2−4z6=0
Solve the equation
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Evaluate
z2−4z6=0
Factor the expression
z2(1−4z4)=0
Separate the equation into 2 possible cases
z2=01−4z4=0
The only way a power can be 0 is when the base equals 0
z=01−4z4=0
Solve the equation
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Evaluate
1−4z4=0
Move the constant to the right-hand side and change its sign
−4z4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−4z4=−1
Change the signs on both sides of the equation
4z4=1
Divide both sides
44z4=41
Divide the numbers
z4=41
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±441
Simplify the expression
z=±22
Separate the equation into 2 possible cases
z=22z=−22
z=0z=22z=−22
z=0z=0z=22z=−22
Find the union
z=0z=22z=−22
Solution
z1=−22,z2=0,z3=22
Alternative Form
z1≈−0.707107,z2=0,z3≈0.707107
Show Solution