Question
Simplify the expression
4x4−24x3+45x2−25x
Evaluate
(2x−5)(2x−5)(x−1)(x×1)
Remove the parentheses
(2x−5)(2x−5)(x−1)x×1
Any expression multiplied by 1 remains the same
(2x−5)(2x−5)(x−1)x
Multiply the first two terms
(2x−5)2(x−1)x
Expand the expression
More Steps

Evaluate
(2x−5)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(2x)2−2×2x×5+52
Calculate
4x2−20x+25
(4x2−20x+25)(x−1)x
Multiply the terms
More Steps

Evaluate
(4x2−20x+25)(x−1)
Apply the distributive property
4x2×x−4x2×1−20x×x−(−20x×1)+25x−25×1
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
4x3−4x2×1−20x×x−(−20x×1)+25x−25×1
Any expression multiplied by 1 remains the same
4x3−4x2−20x×x−(−20x×1)+25x−25×1
Multiply the terms
4x3−4x2−20x2−(−20x×1)+25x−25×1
Any expression multiplied by 1 remains the same
4x3−4x2−20x2−(−20x)+25x−25×1
Any expression multiplied by 1 remains the same
4x3−4x2−20x2−(−20x)+25x−25
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4x3−4x2−20x2+20x+25x−25
Subtract the terms
More Steps

Evaluate
−4x2−20x2
Collect like terms by calculating the sum or difference of their coefficients
(−4−20)x2
Subtract the numbers
−24x2
4x3−24x2+20x+25x−25
Add the terms
More Steps

Evaluate
20x+25x
Collect like terms by calculating the sum or difference of their coefficients
(20+25)x
Add the numbers
45x
4x3−24x2+45x−25
(4x3−24x2+45x−25)x
Apply the distributive property
4x3×x−24x2×x+45x×x−25x
Multiply the terms
More Steps

Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
4x4−24x2×x+45x×x−25x
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
4x4−24x3+45x×x−25x
Solution
4x4−24x3+45x2−25x
Show Solution

Find the roots
x1=0,x2=1,x3=25
Alternative Form
x1=0,x2=1,x3=2.5
Evaluate
(2x−5)(2x−5)(x−1)(x×1)
To find the roots of the expression,set the expression equal to 0
(2x−5)(2x−5)(x−1)(x×1)=0
Any expression multiplied by 1 remains the same
(2x−5)(2x−5)(x−1)x=0
Multiply the first two terms
(2x−5)2(x−1)x=0
Separate the equation into 3 possible cases
(2x−5)2=0x−1=0x=0
Solve the equation
More Steps

Evaluate
(2x−5)2=0
The only way a power can be 0 is when the base equals 0
2x−5=0
Move the constant to the right-hand side and change its sign
2x=0+5
Removing 0 doesn't change the value,so remove it from the expression
2x=5
Divide both sides
22x=25
Divide the numbers
x=25
x=25x−1=0x=0
Solve the equation
More Steps

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=25x=1x=0
Solution
x1=0,x2=1,x3=25
Alternative Form
x1=0,x2=1,x3=2.5
Show Solution
