Question
Simplify the expression
4x8−14x7+10x6
Evaluate
(2x−5)×2x5(x−1)(x×1)
Remove the parentheses
(2x−5)×2x5(x−1)x×1
Rewrite the expression
(2x−5)×2x5(x−1)x
Multiply the terms with the same base by adding their exponents
(2x−5)×2x5+1(x−1)
Add the numbers
(2x−5)×2x6(x−1)
Multiply the first two terms
2x6(2x−5)(x−1)
Multiply the terms
More Steps

Evaluate
2x6(2x−5)
Apply the distributive property
2x6×2x−2x6×5
Multiply the terms
More Steps

Evaluate
2x6×2x
Multiply the numbers
4x6×x
Multiply the terms
4x7
4x7−2x6×5
Multiply the numbers
4x7−10x6
(4x7−10x6)(x−1)
Apply the distributive property
4x7×x−4x7×1−10x6×x−(−10x6×1)
Multiply the terms
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Evaluate
x7×x
Use the product rule an×am=an+m to simplify the expression
x7+1
Add the numbers
x8
4x8−4x7×1−10x6×x−(−10x6×1)
Any expression multiplied by 1 remains the same
4x8−4x7−10x6×x−(−10x6×1)
Multiply the terms
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Evaluate
x6×x
Use the product rule an×am=an+m to simplify the expression
x6+1
Add the numbers
x7
4x8−4x7−10x7−(−10x6×1)
Any expression multiplied by 1 remains the same
4x8−4x7−10x7−(−10x6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4x8−4x7−10x7+10x6
Solution
More Steps

Evaluate
−4x7−10x7
Collect like terms by calculating the sum or difference of their coefficients
(−4−10)x7
Subtract the numbers
−14x7
4x8−14x7+10x6
Show Solution

Find the roots
x1=0,x2=1,x3=25
Alternative Form
x1=0,x2=1,x3=2.5
Evaluate
(2x−5)(2x5)(x−1)(x×1)
To find the roots of the expression,set the expression equal to 0
(2x−5)(2x5)(x−1)(x×1)=0
Multiply the terms
(2x−5)×2x5(x−1)(x×1)=0
Any expression multiplied by 1 remains the same
(2x−5)×2x5(x−1)x=0
Multiply the terms
More Steps

Multiply the terms
(2x−5)×2x5(x−1)x
Multiply the terms with the same base by adding their exponents
(2x−5)×2x5+1(x−1)
Add the numbers
(2x−5)×2x6(x−1)
Multiply the first two terms
2x6(2x−5)(x−1)
2x6(2x−5)(x−1)=0
Elimination the left coefficient
x6(2x−5)(x−1)=0
Separate the equation into 3 possible cases
x6=02x−5=0x−1=0
The only way a power can be 0 is when the base equals 0
x=02x−5=0x−1=0
Solve the equation
More Steps

Evaluate
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=0x=25x−1=0
Solve the equation
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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=0x=25x=1
Solution
x1=0,x2=1,x3=25
Alternative Form
x1=0,x2=1,x3=2.5
Show Solution
