Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
a(10−a)(10+a)
Evaluate
100a−a3
Factor out a from the expression
a(100−a2)
Solution
More Steps
Evaluate
100−a2
Rewrite the expression in exponential form
102−a2
Use a2−b2=(a−b)(a+b) to factor the expression
(10−a)(10+a)
a(10−a)(10+a)
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Find the roots
a1=−10,a2=0,a3=10
Evaluate
100a−a3
To find the roots of the expression,set the expression equal to 0
100a−a3=0
Factor the expression
a(100−a2)=0
Separate the equation into 2 possible cases
a=0100−a2=0
Solve the equation
More Steps
Evaluate
100−a2=0
Move the constant to the right-hand side and change its sign
−a2=0−100
Removing 0 doesn't change the value,so remove it from the expression
−a2=−100
Change the signs on both sides of the equation
a2=100
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±100
Simplify the expression
More Steps
Evaluate
100
Write the number in exponential form with the base of 10
102
Reduce the index of the radical and exponent with 2
10
a=±10
Separate the equation into 2 possible cases
a=10a=−10
a=0a=10a=−10
Solution
a1=−10,a2=0,a3=10
Show Solution