Question
Simplify the expression
36y4−4y2
Evaluate
4y2(9y2−1)
Apply the distributive property
4y2×9y2−4y2×1
Multiply the terms
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Evaluate
4y2×9y2
Multiply the numbers
36y2×y2
Multiply the terms
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Evaluate
y2×y2
Use the product rule an×am=an+m to simplify the expression
y2+2
Add the numbers
y4
36y4
36y4−4y2×1
Solution
36y4−4y2
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Factor the expression
4y2(3y−1)(3y+1)
Evaluate
4y2(9y2−1)
Solution
4y2(3y−1)(3y+1)
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Find the roots
y1=−31,y2=0,y3=31
Alternative Form
y1=−0.3˙,y2=0,y3=0.3˙
Evaluate
4y2(9y2−1)
To find the roots of the expression,set the expression equal to 0
4y2(9y2−1)=0
Elimination the left coefficient
y2(9y2−1)=0
Separate the equation into 2 possible cases
y2=09y2−1=0
The only way a power can be 0 is when the base equals 0
y=09y2−1=0
Solve the equation
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Evaluate
9y2−1=0
Move the constant to the right-hand side and change its sign
9y2=0+1
Removing 0 doesn't change the value,so remove it from the expression
9y2=1
Divide both sides
99y2=91
Divide the numbers
y2=91
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±91
Simplify the expression
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Evaluate
91
To take a root of a fraction,take the root of the numerator and denominator separately
91
Simplify the radical expression
91
Simplify the radical expression
31
y=±31
Separate the equation into 2 possible cases
y=31y=−31
y=0y=31y=−31
Solution
y1=−31,y2=0,y3=31
Alternative Form
y1=−0.3˙,y2=0,y3=0.3˙
Show Solution
