Question
Simplify the expression
480m3−1680m2+1470m
Evaluate
5m(4m−7)×6(4m−7)
Multiply the terms
30m(4m−7)(4m−7)
Multiply the terms
30m(4m−7)2
Expand the expression
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Evaluate
(4m−7)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(4m)2−2×4m×7+72
Calculate
16m2−56m+49
30m(16m2−56m+49)
Apply the distributive property
30m×16m2−30m×56m+30m×49
Multiply the terms
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Evaluate
30m×16m2
Multiply the numbers
480m×m2
Multiply the terms
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Evaluate
m×m2
Use the product rule an×am=an+m to simplify the expression
m1+2
Add the numbers
m3
480m3
480m3−30m×56m+30m×49
Multiply the terms
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Evaluate
30m×56m
Multiply the numbers
1680m×m
Multiply the terms
1680m2
480m3−1680m2+30m×49
Solution
480m3−1680m2+1470m
Show Solution

Find the roots
m1=0,m2=47
Alternative Form
m1=0,m2=1.75
Evaluate
5m(4m−7)×6(4m−7)
To find the roots of the expression,set the expression equal to 0
5m(4m−7)×6(4m−7)=0
Multiply the terms
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Multiply the terms
5m(4m−7)×6(4m−7)
Multiply the terms
30m(4m−7)(4m−7)
Multiply the terms
30m(4m−7)2
30m(4m−7)2=0
Elimination the left coefficient
m(4m−7)2=0
Separate the equation into 2 possible cases
m=0(4m−7)2=0
Solve the equation
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Evaluate
(4m−7)2=0
The only way a power can be 0 is when the base equals 0
4m−7=0
Move the constant to the right-hand side and change its sign
4m=0+7
Removing 0 doesn't change the value,so remove it from the expression
4m=7
Divide both sides
44m=47
Divide the numbers
m=47
m=0m=47
Solution
m1=0,m2=47
Alternative Form
m1=0,m2=1.75
Show Solution
