Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2x−x2
Evaluate
1−(1−x)(1−x)
Multiply the terms
1−(1−x)2
Expand the expression
1−1+2x−x2
Solution
2x−x2
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Factor the expression
x(2−x)
Evaluate
1−(1−x)(1−x)
Evaluate
1−(1−x)2
Rewrite the expression in exponential form
12−(1−x)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−(1−x))(1+1−x)
Evaluate
More Steps
Evaluate
1−(1−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
1−1+x
Since two opposites add up to 0,remove them form the expression
x
x(1+1−x)
Solution
x(2−x)
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Find the roots
x1=0,x2=2
Evaluate
1−(1−x)(1−x)
To find the roots of the expression,set the expression equal to 0
1−(1−x)(1−x)=0
Multiply the terms
1−(1−x)2=0
Move the constant to the right-hand side and change its sign
−(1−x)2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−(1−x)2=−1
Change the signs on both sides of the equation
(1−x)2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
1−x=±1
Simplify the expression
1−x=±1
Separate the equation into 2 possible cases
1−x=11−x=−1
Calculate
More Steps
Evaluate
1−x=1
Move the constant to the right-hand side and change its sign
−x=1−1
Subtract the terms
−x=0
Change the signs on both sides of the equation
x=0
x=01−x=−1
Calculate
More Steps
Evaluate
1−x=−1
Move the constant to the right-hand side and change its sign
−x=−1−1
Subtract the numbers
−x=−2
Change the signs on both sides of the equation
x=2
x=0x=2
Solution
x1=0,x2=2
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