Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
6y3−60y2+150y
Evaluate
2(y−5)2y×12
Multiply the terms
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Multiply the terms
2(y−5)2y
Multiply the terms
2(y−5)2y
Use the commutative property to reorder the terms
2y(y−5)2
2y(y−5)2×12
Cancel out the common factor 2
y(y−5)2×6
Use the commutative property to reorder the terms
6y(y−5)2
Expand the expression
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Evaluate
(y−5)2
Use (a−b)2=a2−2ab+b2 to expand the expression
y2−2y×5+52
Calculate
y2−10y+25
6y(y2−10y+25)
Apply the distributive property
6y×y2−6y×10y+6y×25
Multiply the terms
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Evaluate
y×y2
Use the product rule an×am=an+m to simplify the expression
y1+2
Add the numbers
y3
6y3−6y×10y+6y×25
Multiply the terms
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Evaluate
6y×10y
Multiply the numbers
60y×y
Multiply the terms
60y2
6y3−60y2+6y×25
Solution
6y3−60y2+150y
Show Solution
Find the roots
y1=0,y2=5
Evaluate
2(y−5)2y×12
To find the roots of the expression,set the expression equal to 0
2(y−5)2y×12=0
Multiply the terms
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Multiply the terms
2(y−5)2y×12
Multiply the terms
More Steps
Multiply the terms
2(y−5)2y
Multiply the terms
2(y−5)2y
Use the commutative property to reorder the terms
2y(y−5)2
2y(y−5)2×12
Cancel out the common factor 2
y(y−5)2×6
Use the commutative property to reorder the terms
6y(y−5)2
6y(y−5)2=0
Elimination the left coefficient
y(y−5)2=0
Separate the equation into 2 possible cases
y=0(y−5)2=0
Solve the equation
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Evaluate
(y−5)2=0
The only way a power can be 0 is when the base equals 0
y−5=0
Move the constant to the right-hand side and change its sign
y=0+5
Removing 0 doesn't change the value,so remove it from the expression
y=5
y=0y=5
Solution
y1=0,y2=5
Show Solution