Simplify ( square root of y- square root of 2)^2

Math
(y-2)2
Rewrite (y-2)2 as (y-2)(y-2).
(y-2)(y-2)
Expand (y-2)(y-2) using the FOIL Method.
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Apply the distributive property.
y(y-2)-2(y-2)
Apply the distributive property.
yy+y(-2)-2(y-2)
Apply the distributive property.
yy+y(-2)-2y-2(-2)
yy+y(-2)-2y-2(-2)
Simplify and combine like terms.
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Simplify each term.
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Multiply yy.
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Raise y to the power of 1.
y1y+y(-2)-2y-2(-2)
Raise y to the power of 1.
y1y1+y(-2)-2y-2(-2)
Use the power rule aman=am+n to combine exponents.
y1+1+y(-2)-2y-2(-2)
Add 1 and 1.
y2+y(-2)-2y-2(-2)
y2+y(-2)-2y-2(-2)
Rewrite y2 as y.
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Use axn=axn to rewrite y as y12.
(y12)2+y(-2)-2y-2(-2)
Apply the power rule and multiply exponents, (am)n=amn.
y12⋅2+y(-2)-2y-2(-2)
Combine 12 and 2.
y22+y(-2)-2y-2(-2)
Cancel the common factor of 2.
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Cancel the common factor.
y22+y(-2)-2y-2(-2)
Divide 1 by 1.
y1+y(-2)-2y-2(-2)
y1+y(-2)-2y-2(-2)
Simplify.
y+y(-2)-2y-2(-2)
y+y(-2)-2y-2(-2)
Combine using the product rule for radicals.
y-y⋅2-2y-2(-2)
Combine using the product rule for radicals.
y-y⋅2-y⋅2-2(-2)
Multiply -2(-2).
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Multiply -1 by -1.
y-y⋅2-y⋅2+122
Multiply 2 by 1.
y-y⋅2-y⋅2+22
Raise 2 to the power of 1.
y-y⋅2-y⋅2+212
Raise 2 to the power of 1.
y-y⋅2-y⋅2+2121
Use the power rule aman=am+n to combine exponents.
y-y⋅2-y⋅2+21+1
Add 1 and 1.
y-y⋅2-y⋅2+22
y-y⋅2-y⋅2+22
Rewrite 22 as 2.
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Use axn=axn to rewrite 2 as 212.
y-y⋅2-y⋅2+(212)2
Apply the power rule and multiply exponents, (am)n=amn.
y-y⋅2-y⋅2+212⋅2
Combine 12 and 2.
y-y⋅2-y⋅2+222
Cancel the common factor of 2.
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Cancel the common factor.
y-y⋅2-y⋅2+222
Divide 1 by 1.
y-y⋅2-y⋅2+21
y-y⋅2-y⋅2+21
Evaluate the exponent.
y-y⋅2-y⋅2+2
y-y⋅2-y⋅2+2
y-y⋅2-y⋅2+2
Subtract y⋅2 from -y⋅2.
y-2y⋅2+2
y-2y⋅2+2
Reorder factors in y-2y⋅2+2.
y-22y+2
Simplify ( square root of y- square root of 2)^2

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