Question
Simplify the expression
8a5−24a3
Evaluate
(2a2×4a3)−(3a3×8)
Multiply
More Steps

Multiply the terms
2a2×4a3
Multiply the terms
8a2×a3
Multiply the terms with the same base by adding their exponents
8a2+3
Add the numbers
8a5
8a5−(3a3×8)
Solution
8a5−24a3
Show Solution

Factor the expression
8a3(a2−3)
Evaluate
(2a2×4a3)−(3a3×8)
Multiply
More Steps

Multiply the terms
2a2×4a3
Multiply the terms
8a2×a3
Multiply the terms with the same base by adding their exponents
8a2+3
Add the numbers
8a5
8a5−(3a3×8)
Multiply the terms
8a5−24a3
Rewrite the expression
8a3×a2−8a3×3
Solution
8a3(a2−3)
Show Solution

Find the roots
a1=−3,a2=0,a3=3
Alternative Form
a1≈−1.732051,a2=0,a3≈1.732051
Evaluate
(2a2×4a3)−(3a3×8)
To find the roots of the expression,set the expression equal to 0
(2a2×4a3)−(3a3×8)=0
Multiply
More Steps

Multiply the terms
2a2×4a3
Multiply the terms
8a2×a3
Multiply the terms with the same base by adding their exponents
8a2+3
Add the numbers
8a5
8a5−(3a3×8)=0
Multiply the terms
8a5−24a3=0
Factor the expression
8a3(a2−3)=0
Divide both sides
a3(a2−3)=0
Separate the equation into 2 possible cases
a3=0a2−3=0
The only way a power can be 0 is when the base equals 0
a=0a2−3=0
Solve the equation
More Steps

Evaluate
a2−3=0
Move the constant to the right-hand side and change its sign
a2=0+3
Removing 0 doesn't change the value,so remove it from the expression
a2=3
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±3
Separate the equation into 2 possible cases
a=3a=−3
a=0a=3a=−3
Solution
a1=−3,a2=0,a3=3
Alternative Form
a1≈−1.732051,a2=0,a3≈1.732051
Show Solution
