Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
3x−x2−2
Evaluate
(x−1)(2−x)
Solution
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Evaluate
(x−1)(2−x)
Apply the distributive property
x×2−x×x−2−(−x)
Use the commutative property to reorder the terms
2x−x×x−2−(−x)
Multiply the terms
2x−x2−2−(−x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x−x2−2+x
Add the terms
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Evaluate
2x+x
Collect like terms by calculating the sum or difference of their coefficients
(2+1)x
Add the numbers
3x
3x−x2−2
3x−x2−2
Show Solution
Find the roots
x1=1,x2=2
Evaluate
(x−1)(2−x)
To find the roots of the expression,set the expression equal to 0
(x−1)(2−x)=0
Find the domain
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Evaluate
(x−1)(2−x)≥0
Separate the inequality into 2 possible cases
{x−1≥02−x≥0{x−1≤02−x≤0
Solve the inequality
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Evaluate
x−1≥0
Move the constant to the right side
x≥0+1
Removing 0 doesn't change the value,so remove it from the expression
x≥1
{x≥12−x≥0{x−1≤02−x≤0
Solve the inequality
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Evaluate
2−x≥0
Move the constant to the right side
−x≥0−2
Removing 0 doesn't change the value,so remove it from the expression
−x≥−2
Change the signs on both sides of the inequality and flip the inequality sign
x≤2
{x≥1x≤2{x−1≤02−x≤0
Solve the inequality
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Evaluate
x−1≤0
Move the constant to the right side
x≤0+1
Removing 0 doesn't change the value,so remove it from the expression
x≤1
{x≥1x≤2{x≤12−x≤0
Solve the inequality
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Evaluate
2−x≤0
Move the constant to the right side
−x≤0−2
Removing 0 doesn't change the value,so remove it from the expression
−x≤−2
Change the signs on both sides of the inequality and flip the inequality sign
x≥2
{x≥1x≤2{x≤1x≥2
Find the intersection
1≤x≤2{x≤1x≥2
Find the intersection
1≤x≤2x∈∅
Find the union
1≤x≤2
(x−1)(2−x)=0,1≤x≤2
Calculate
(x−1)(2−x)=0
The only way a root could be 0 is when the radicand equals 0
(x−1)(2−x)=0
Separate the equation into 2 possible cases
x−1=02−x=0
Solve the equation
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Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=12−x=0
Solve the equation
More Steps
Evaluate
2−x=0
Move the constant to the right-hand side and change its sign
−x=0−2
Removing 0 doesn't change the value,so remove it from the expression
−x=−2
Change the signs on both sides of the equation
x=2
x=1x=2
Check if the solution is in the defined range
x=1x=2,1≤x≤2
Find the intersection of the solution and the defined range
x=1x=2
Solution
x1=1,x2=2
Show Solution