Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
32x8−x−4x28−x
Evaluate
2(8−x)×2(x8−x)
Remove the parentheses
2(8−x)×2x8−x
Multiply the terms
4(8−x)x8−x
Multiply the terms
4x8−x×(8−x)
Apply the distributive property
4x8−x×8+4x8−x×(−x)
Calculate
32x8−x+4x8−x×(−x)
Solution
More Steps
Evaluate
4x8−x×(−x)
Rewrite the expression
−4x8−x×x
Multiply the terms
−4x28−x
32x8−x−4x28−x
Show Solution
Find the roots
x1=0,x2=8
Evaluate
2(8−x)×2(x8−x)
To find the roots of the expression,set the expression equal to 0
2(8−x)×2(x8−x)=0
Find the domain
More Steps
Evaluate
8−x≥0
Move the constant to the right side
−x≥0−8
Removing 0 doesn't change the value,so remove it from the expression
−x≥−8
Change the signs on both sides of the inequality and flip the inequality sign
x≤8
2(8−x)×2(x8−x)=0,x≤8
Calculate
2(8−x)×2(x8−x)=0
Multiply the terms
2(8−x)×2x8−x=0
Multiply
More Steps
Multiply the terms
2(8−x)×2x8−x
Multiply the terms
4(8−x)x8−x
Multiply the terms
4x8−x×(8−x)
4x8−x×(8−x)=0
Elimination the left coefficient
x8−x×(8−x)=0
Separate the equation into 3 possible cases
x=08−x=08−x=0
Solve the equation
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Evaluate
8−x=0
The only way a root could be 0 is when the radicand equals 0
8−x=0
Move the constant to the right-hand side and change its sign
−x=0−8
Removing 0 doesn't change the value,so remove it from the expression
−x=−8
Change the signs on both sides of the equation
x=8
x=0x=88−x=0
Solve the equation
More Steps
Evaluate
8−x=0
Move the constant to the right-hand side and change its sign
−x=0−8
Removing 0 doesn't change the value,so remove it from the expression
−x=−8
Change the signs on both sides of the equation
x=8
x=0x=8x=8
Find the union
x=0x=8
Check if the solution is in the defined range
x=0x=8,x≤8
Find the intersection of the solution and the defined range
x=0x=8
Solution
x1=0,x2=8
Show Solution