Question
Simplify the expression
34x6−40x5+100x4
Evaluate
(12×9x−5)x4(x−5)
Remove the parentheses
12×9x−5×x4(x−5)
Multiply the terms
More Steps

Evaluate
12×9x−5×x4
Multiply the terms
More Steps

Multiply the terms
12×9x−5
Cancel out the common factor 3
4×3x−5
Multiply the terms
34(x−5)
34(x−5)x4
Multiply the terms
34(x−5)x4
34(x−5)x4(x−5)
Multiply the terms
34(x−5)x4(x−5)
Multiply the terms
34(x−5)2x4
Solution
More Steps

Evaluate
4(x−5)2x4
Expand the expression
More Steps

Evaluate
(x−5)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×5+52
Calculate
x2−10x+25
4(x2−10x+25)x4
Multiply the terms
More Steps

Evaluate
4(x2−10x+25)
Apply the distributive property
4x2−4×10x+4×25
Multiply the numbers
4x2−40x+4×25
Multiply the numbers
4x2−40x+100
(4x2−40x+100)x4
Apply the distributive property
4x2×x4−40x×x4+100x4
Multiply the terms
More Steps

Evaluate
x2×x4
Use the product rule an×am=an+m to simplify the expression
x2+4
Add the numbers
x6
4x6−40x×x4+100x4
Multiply the terms
More Steps

Evaluate
x×x4
Use the product rule an×am=an+m to simplify the expression
x1+4
Add the numbers
x5
4x6−40x5+100x4
34x6−40x5+100x4
Show Solution

Find the roots
x1=0,x2=5
Evaluate
(12×9x−5)(x4)(x−5)
To find the roots of the expression,set the expression equal to 0
(12×9x−5)(x4)(x−5)=0
Multiply the terms
More Steps

Multiply the terms
12×9x−5
Cancel out the common factor 3
4×3x−5
Multiply the terms
34(x−5)
34(x−5)(x4)(x−5)=0
Calculate
34(x−5)x4(x−5)=0
Multiply the terms
More Steps

Multiply the terms
34(x−5)x4(x−5)
Multiply the terms
34(x−5)x4(x−5)
Multiply the terms
34(x−5)x4(x−5)
Multiply the terms
34(x−5)2x4
34(x−5)2x4=0
Simplify
4(x−5)2x4=0
Elimination the left coefficient
(x−5)2x4=0
Separate the equation into 2 possible cases
(x−5)2=0x4=0
Solve the equation
More Steps

Evaluate
(x−5)2=0
The only way a power can be 0 is when the base equals 0
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=5x4=0
The only way a power can be 0 is when the base equals 0
x=5x=0
Solution
x1=0,x2=5
Show Solution
