Question
Simplify the expression
42a7−6a6−18a8
Evaluate
6a4(7a3−a2−3a4)
Apply the distributive property
6a4×7a3−6a4×a2−6a4×3a4
Multiply the terms
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Evaluate
6a4×7a3
Multiply the numbers
42a4×a3
Multiply the terms
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Evaluate
a4×a3
Use the product rule an×am=an+m to simplify the expression
a4+3
Add the numbers
a7
42a7
42a7−6a4×a2−6a4×3a4
Multiply the terms
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Evaluate
a4×a2
Use the product rule an×am=an+m to simplify the expression
a4+2
Add the numbers
a6
42a7−6a6−6a4×3a4
Solution
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Evaluate
6a4×3a4
Multiply the numbers
18a4×a4
Multiply the terms
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Evaluate
a4×a4
Use the product rule an×am=an+m to simplify the expression
a4+4
Add the numbers
a8
18a8
42a7−6a6−18a8
Show Solution

Factor the expression
6a6(7a−1−3a2)
Evaluate
6a4(7a3−a2−3a4)
Factor the expression
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Evaluate
7a3−a2−3a4
Rewrite the expression
a2×7a−a2−a2×3a2
Factor out a2 from the expression
a2(7a−1−3a2)
6a4×a2(7a−1−3a2)
Solution
6a6(7a−1−3a2)
Show Solution

Find the roots
a1=0,a2=67−37,a3=67+37
Alternative Form
a1=0,a2≈0.152873,a3≈2.18046
Evaluate
6a4(7a3−a2−3a4)
To find the roots of the expression,set the expression equal to 0
6a4(7a3−a2−3a4)=0
Elimination the left coefficient
a4(7a3−a2−3a4)=0
Separate the equation into 2 possible cases
a4=07a3−a2−3a4=0
The only way a power can be 0 is when the base equals 0
a=07a3−a2−3a4=0
Solve the equation
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Evaluate
7a3−a2−3a4=0
Factor the expression
a2(7a−1−3a2)=0
Separate the equation into 2 possible cases
a2=07a−1−3a2=0
The only way a power can be 0 is when the base equals 0
a=07a−1−3a2=0
Solve the equation
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Evaluate
7a−1−3a2=0
Rewrite in standard form
−3a2+7a−1=0
Multiply both sides
3a2−7a+1=0
Substitute a=3,b=−7 and c=1 into the quadratic formula a=2a−b±b2−4ac
a=2×37±(−7)2−4×3
Simplify the expression
a=67±(−7)2−4×3
Simplify the expression
a=67±37
Separate the equation into 2 possible cases
a=67+37a=67−37
a=0a=67+37a=67−37
a=0a=0a=67+37a=67−37
Find the union
a=0a=67+37a=67−37
Solution
a1=0,a2=67−37,a3=67+37
Alternative Form
a1=0,a2≈0.152873,a3≈2.18046
Show Solution
