Question
Simplify the expression
q5−q4
Evaluate
(q−1)q2×q2
Multiply the terms with the same base by adding their exponents
(q−1)q2+2
Add the numbers
(q−1)q4
Multiply the terms
q4(q−1)
Apply the distributive property
q4×q−q4×1
Multiply the terms
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Evaluate
q4×q
Use the product rule an×am=an+m to simplify the expression
q4+1
Add the numbers
q5
q5−q4×1
Solution
q5−q4
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Find the roots
q1=0,q2=1
Evaluate
(q−1)(q2)(q2)
To find the roots of the expression,set the expression equal to 0
(q−1)(q2)(q2)=0
Calculate
(q−1)q2(q2)=0
Calculate
(q−1)q2×q2=0
Multiply the terms
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Multiply the terms
(q−1)q2×q2
Multiply the terms with the same base by adding their exponents
(q−1)q2+2
Add the numbers
(q−1)q4
Multiply the terms
q4(q−1)
q4(q−1)=0
Separate the equation into 2 possible cases
q4=0q−1=0
The only way a power can be 0 is when the base equals 0
q=0q−1=0
Solve the equation
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Evaluate
q−1=0
Move the constant to the right-hand side and change its sign
q=0+1
Removing 0 doesn't change the value,so remove it from the expression
q=1
q=0q=1
Solution
q1=0,q2=1
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