Question
Simplify the expression
−80a3+20a4+60a2
Evaluate
−10a(a−1)×2a(3−a)
Multiply the terms
−20a(a−1)a(3−a)
Multiply the terms
−20a2(a−1)(3−a)
Multiply the terms
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Evaluate
−20a2(a−1)
Apply the distributive property
−20a2×a−(−20a2×1)
Multiply the terms
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Evaluate
a2×a
Use the product rule an×am=an+m to simplify the expression
a2+1
Add the numbers
a3
−20a3−(−20a2×1)
Any expression multiplied by 1 remains the same
−20a3−(−20a2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−20a3+20a2
(−20a3+20a2)(3−a)
Apply the distributive property
−20a3×3−(−20a3×a)+20a2×3−20a2×a
Multiply the numbers
−60a3−(−20a3×a)+20a2×3−20a2×a
Multiply the terms
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Evaluate
a3×a
Use the product rule an×am=an+m to simplify the expression
a3+1
Add the numbers
a4
−60a3−(−20a4)+20a2×3−20a2×a
Multiply the numbers
−60a3−(−20a4)+60a2−20a2×a
Multiply the terms
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Evaluate
a2×a
Use the product rule an×am=an+m to simplify the expression
a2+1
Add the numbers
a3
−60a3−(−20a4)+60a2−20a3
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−60a3+20a4+60a2−20a3
Solution
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Evaluate
−60a3−20a3
Collect like terms by calculating the sum or difference of their coefficients
(−60−20)a3
Subtract the numbers
−80a3
−80a3+20a4+60a2
Show Solution

Find the roots
a1=0,a2=1,a3=3
Evaluate
−10a(a−1)×2a(3−a)
To find the roots of the expression,set the expression equal to 0
−10a(a−1)×2a(3−a)=0
Multiply
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Multiply the terms
−10a(a−1)×2a(3−a)
Multiply the terms
−20a(a−1)a(3−a)
Multiply the terms
−20a2(a−1)(3−a)
−20a2(a−1)(3−a)=0
Change the sign
20a2(a−1)(3−a)=0
Elimination the left coefficient
a2(a−1)(3−a)=0
Separate the equation into 3 possible cases
a2=0a−1=03−a=0
The only way a power can be 0 is when the base equals 0
a=0a−1=03−a=0
Solve the equation
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Evaluate
a−1=0
Move the constant to the right-hand side and change its sign
a=0+1
Removing 0 doesn't change the value,so remove it from the expression
a=1
a=0a=13−a=0
Solve the equation
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Evaluate
3−a=0
Move the constant to the right-hand side and change its sign
−a=0−3
Removing 0 doesn't change the value,so remove it from the expression
−a=−3
Change the signs on both sides of the equation
a=3
a=0a=1a=3
Solution
a1=0,a2=1,a3=3
Show Solution
