Question
Simplify the expression
12a4−54a3
Evaluate
3a2(4a2−2a×9)
Multiply the terms
3a2(4a2−18a)
Apply the distributive property
3a2×4a2−3a2×18a
Multiply the terms
More Steps

Evaluate
3a2×4a2
Multiply the numbers
12a2×a2
Multiply the terms
More Steps

Evaluate
a2×a2
Use the product rule an×am=an+m to simplify the expression
a2+2
Add the numbers
a4
12a4
12a4−3a2×18a
Solution
More Steps

Evaluate
3a2×18a
Multiply the numbers
54a2×a
Multiply the terms
More Steps

Evaluate
a2×a
Use the product rule an×am=an+m to simplify the expression
a2+1
Add the numbers
a3
54a3
12a4−54a3
Show Solution

Factor the expression
6a3(2a−9)
Evaluate
3a2(4a2−2a×9)
Multiply the terms
3a2(4a2−18a)
Factor the expression
More Steps

Evaluate
4a2−18a
Rewrite the expression
2a×2a−2a×9
Factor out 2a from the expression
2a(2a−9)
3a2×2a(2a−9)
Solution
6a3(2a−9)
Show Solution

Find the roots
a1=0,a2=29
Alternative Form
a1=0,a2=4.5
Evaluate
(3a2)(4a2−2a×9)
To find the roots of the expression,set the expression equal to 0
(3a2)(4a2−2a×9)=0
Multiply the terms
3a2(4a2−2a×9)=0
Multiply the terms
3a2(4a2−18a)=0
Elimination the left coefficient
a2(4a2−18a)=0
Separate the equation into 2 possible cases
a2=04a2−18a=0
The only way a power can be 0 is when the base equals 0
a=04a2−18a=0
Solve the equation
More Steps

Evaluate
4a2−18a=0
Factor the expression
More Steps

Evaluate
4a2−18a
Rewrite the expression
2a×2a−2a×9
Factor out 2a from the expression
2a(2a−9)
2a(2a−9)=0
When the product of factors equals 0,at least one factor is 0
2a=02a−9=0
Solve the equation for a
a=02a−9=0
Solve the equation for a
More Steps

Evaluate
2a−9=0
Move the constant to the right-hand side and change its sign
2a=0+9
Removing 0 doesn't change the value,so remove it from the expression
2a=9
Divide both sides
22a=29
Divide the numbers
a=29
a=0a=29
a=0a=0a=29
Find the union
a=0a=29
Solution
a1=0,a2=29
Alternative Form
a1=0,a2=4.5
Show Solution
