Question
Factor the expression
2(y−3)(y+3)
Evaluate
2y2−18
Factor out 2 from the expression
2(y2−9)
Solution
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Evaluate
y2−9
Rewrite the expression in exponential form
y2−32
Use a2−b2=(a−b)(a+b) to factor the expression
(y−3)(y+3)
2(y−3)(y+3)
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Find the roots
y1=−3,y2=3
Evaluate
2y2−18
To find the roots of the expression,set the expression equal to 0
2y2−18=0
Move the constant to the right-hand side and change its sign
2y2=0+18
Removing 0 doesn't change the value,so remove it from the expression
2y2=18
Divide both sides
22y2=218
Divide the numbers
y2=218
Divide the numbers
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Evaluate
218
Reduce the numbers
19
Calculate
9
y2=9
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±9
Simplify the expression
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Evaluate
9
Write the number in exponential form with the base of 3
32
Reduce the index of the radical and exponent with 2
3
y=±3
Separate the equation into 2 possible cases
y=3y=−3
Solution
y1=−3,y2=3
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