Question
Factor the expression
2(y−5)(y+5)
Evaluate
2y2−50
Factor out 2 from the expression
2(y2−25)
Solution
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Evaluate
y2−25
Rewrite the expression in exponential form
y2−52
Use a2−b2=(a−b)(a+b) to factor the expression
(y−5)(y+5)
2(y−5)(y+5)
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Find the roots
y1=−5,y2=5
Evaluate
2y2−50
To find the roots of the expression,set the expression equal to 0
2y2−50=0
Move the constant to the right-hand side and change its sign
2y2=0+50
Removing 0 doesn't change the value,so remove it from the expression
2y2=50
Divide both sides
22y2=250
Divide the numbers
y2=250
Divide the numbers
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Evaluate
250
Reduce the numbers
125
Calculate
25
y2=25
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±25
Simplify the expression
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Evaluate
25
Write the number in exponential form with the base of 5
52
Reduce the index of the radical and exponent with 2
5
y=±5
Separate the equation into 2 possible cases
y=5y=−5
Solution
y1=−5,y2=5
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