Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4x65x−125x×x5
Evaluate
(5x×1×4)(x−3)x5
Remove the parentheses
5x×1×4(x−3)x5
Multiply the terms
5x×4(x−3)x5
Calculate the product
45x×x5(x−3)
Multiply the terms
More Steps
Evaluate
5x×(x−3)
Multiply each term in the parentheses by 5x
5x×x+5x×(−3)
Calculate the product
x5x+5x×(−3)
Calculate the product
x5x−35x
4(x5x−35x)x5
Multiply the terms
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Evaluate
(x5x−35x)×4
Use the the distributive property to expand the expression
x5x×4−35x×4
Use the commutative property to reorder the terms
4x5x−35x×4
Multiply the terms
4x5x−125x
(4x5x−125x)x5
Use the the distributive property to expand the expression
4x5x×x5−125x×x5
Solution
More Steps
Evaluate
x×x5
Use the product rule an×am=an+m to simplify the expression
x1+5
Add the numbers
x6
4x65x−125x×x5
Show Solution
Factor the expression
4x55x×(x−3)
Evaluate
(5x×1×4)(x−3)x5
Remove the parentheses
5x×1×4(x−3)x5
Multiply the terms
5x×4(x−3)x5
Calculate the product
More Steps
Evaluate
1×4
Any expression multiplied by 1 remains the same
4
Evaluate
45x
45x×(x−3)x5
Multiply the terms
45x×x5(x−3)
Multiply the terms
4(x5x−35x)x5
Factor out 5x from the expression
4(x−3)5x×x5
Solution
4x55x×(x−3)
Show Solution
Find the roots
x1=0,x2=3
Evaluate
(5x×1×4)(x−3)(x5)
To find the roots of the expression,set the expression equal to 0
(5x×1×4)(x−3)(x5)=0
Find the domain
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Evaluate
5x×1≥0
Multiply the terms
5x≥0
Rewrite the expression
x≥0
(5x×1×4)(x−3)(x5)=0,x≥0
Calculate
(5x×1×4)(x−3)(x5)=0
Multiply the terms
(5x×4)(x−3)(x5)=0
Calculate the product
45x×(x−3)(x5)=0
Calculate
45x×(x−3)x5=0
Separate the equation into 3 possible cases
5x=0x−3=0x5=0
Solve the equation
More Steps
Evaluate
5x=0
The only way a root could be 0 is when the radicand equals 0
5x=0
Rewrite the expression
x=0
x=0x−3=0x5=0
Solve the equation
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=0x=3x5=0
The only way a power can be 0 is when the base equals 0
x=0x=3x=0
Find the union
x=0x=3
Check if the solution is in the defined range
x=0x=3,x≥0
Find the intersection of the solution and the defined range
x=0x=3
Solution
x1=0,x2=3
Show Solution