Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4−2a−a+a2
Evaluate
2−a1−2a−21
Reduce fractions to a common denominator
(2−a)×22−2(2−a)a(2−a)−2(2−a)2−a
Use the commutative property to reorder the terms
2(2−a)2−2(2−a)a(2−a)−2(2−a)2−a
Write all numerators above the common denominator
2(2−a)2−a(2−a)−(2−a)
Multiply the terms
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Evaluate
a(2−a)
Apply the distributive property
a×2−a×a
Use the commutative property to reorder the terms
2a−a×a
Multiply the terms
2a−a2
2(2−a)2−(2a−a2)−(2−a)
Subtract the terms
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Evaluate
2−(2a−a2)−(2−a)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2−2a+a2−(2−a)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2−2a+a2−2+a
Since two opposites add up to 0,remove them form the expression
−2a+a2+a
Add the terms
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Evaluate
−2a+a
Collect like terms by calculating the sum or difference of their coefficients
(−2+1)a
Add the numbers
−a
−a+a2
2(2−a)−a+a2
Solution
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Evaluate
2(2−a)
Apply the distributive property
2×2−2a
Multiply the numbers
4−2a
4−2a−a+a2
Show Solution
Find the excluded values
a=2
Evaluate
2−a1−2a−21
To find the excluded values,set the denominators equal to 0
2−a=0
Move the constant to the right-hand side and change its sign
−a=0−2
Removing 0 doesn't change the value,so remove it from the expression
−a=−2
Solution
a=2
Show Solution
Find the roots
a1=0,a2=1
Evaluate
2−a1−2a−21
To find the roots of the expression,set the expression equal to 0
2−a1−2a−21=0
Find the domain
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Evaluate
2−a=0
Move the constant to the right side
−a=0−2
Removing 0 doesn't change the value,so remove it from the expression
−a=−2
Change the signs on both sides of the equation
a=2
2−a1−2a−21=0,a=2
Calculate
2−a1−2a−21=0
Subtract the terms
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Simplify
2−a1−2a
Reduce fractions to a common denominator
(2−a)×22−2(2−a)a(2−a)
Use the commutative property to reorder the terms
2(2−a)2−2(2−a)a(2−a)
Write all numerators above the common denominator
2(2−a)2−a(2−a)
Multiply the terms
More Steps
Evaluate
a(2−a)
Apply the distributive property
a×2−a×a
Use the commutative property to reorder the terms
2a−a×a
Multiply the terms
2a−a2
2(2−a)2−(2a−a2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2(2−a)2−2a+a2
2(2−a)2−2a+a2−21=0
Subtract the terms
More Steps
Simplify
2(2−a)2−2a+a2−21
Reduce fractions to a common denominator
2(2−a)2−2a+a2−2(2−a)2−a
Write all numerators above the common denominator
2(2−a)2−2a+a2−(2−a)
Calculate the sum or difference
More Steps
Evaluate
2−2a+a2−(2−a)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2−2a+a2−2+a
Since two opposites add up to 0,remove them form the expression
−2a+a2+a
Add the terms
−a+a2
2(2−a)−a+a2
2(2−a)−a+a2=0
Cross multiply
−a+a2=2(2−a)×0
Simplify the equation
−a+a2=0
Factor the expression
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Evaluate
−a+a2
Rewrite the expression
−a+a×a
Factor out −a from the expression
−a(1−a)
−a(1−a)=0
When the product of factors equals 0,at least one factor is 0
−a=01−a=0
Solve the equation for a
a=01−a=0
Solve the equation for a
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Evaluate
1−a=0
Move the constant to the right-hand side and change its sign
−a=0−1
Removing 0 doesn't change the value,so remove it from the expression
−a=−1
Change the signs on both sides of the equation
a=1
a=0a=1
Check if the solution is in the defined range
a=0a=1,a=2
Find the intersection of the solution and the defined range
a=0a=1
Solution
a1=0,a2=1
Show Solution