Algebra
Calculus
Trigonometry
Matrix
Question
y(y−5)×9(y−5)
Simplify the expression
9y3−90y2+225y
Evaluate
y(y−5)×9(y−5)
Use the commutative property to reorder the terms
9y(y−5)(y−5)
Multiply the terms
9y(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
9y(y2−10y+25)
Apply the distributive property
9y×y2−9y×10y+9y×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
9y3−9y×10y+9y×25
Multiply the terms
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Evaluate
9y×10y
Multiply the numbers
90y×y
Multiply the terms
90y2
9y3−90y2+9y×25
Solution
9y3−90y2+225y
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Find the roots
y1=0,y2=5
Evaluate
y(y−5)×9(y−5)
To find the roots of the expression,set the expression equal to 0
y(y−5)×9(y−5)=0
Multiply the terms
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Multiply the terms
y(y−5)×9(y−5)
Use the commutative property to reorder the terms
9y(y−5)(y−5)
Multiply the terms
9y(y−5)2
9y(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