Factor y-b-(y-b)^2

Math
y-b-(y-b)2
Factor -1 out of y-b-(y-b)2.
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Reorder the expression.
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Reorder y and -b.
y-b-(-b+y)2
Move y.
-b-(-b+y)2+y
Reorder -b and -(-b+y)2.
-(-b+y)2-b+y
-(-b+y)2-b+y
Factor -1 out of -(-b+y)2.
-((-b+y)2)-b+y
Factor -1 out of -b.
-((-b+y)2)-(b)+y
Factor -1 out of y.
-((-b+y)2)-(b)-1(-y)
Factor -1 out of -((-b+y)2)-(b).
-((-b+y)2+b)-1(-y)
Factor -1 out of -((-b+y)2+b)-1(-y).
-((-b+y)2+b-y)
-((-b+y)2+b-y)
Rewrite (-b+y)2 as (-b+y)(-b+y).
-((-b+y)(-b+y)+b-y)
Expand (-b+y)(-b+y) using the FOIL Method.
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Apply the distributive property.
-(-b(-b+y)+y(-b+y)+b-y)
Apply the distributive property.
-(-b(-b)-by+y(-b+y)+b-y)
Apply the distributive property.
-(-b(-b)-by+y(-b)+y⋅y+b-y)
-(-b(-b)-by+y(-b)+y⋅y+b-y)
Simplify and combine like terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
-(-1⋅-1b⋅b-by+y(-b)+y⋅y+b-y)
Multiply b by b by adding the exponents.
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Move b.
-(-1⋅-1(b⋅b)-by+y(-b)+y⋅y+b-y)
Multiply b by b.
-(-1⋅-1b2-by+y(-b)+y⋅y+b-y)
-(-1⋅-1b2-by+y(-b)+y⋅y+b-y)
Multiply -1 by -1.
-(1b2-by+y(-b)+y⋅y+b-y)
Multiply b2 by 1.
-(b2-by+y(-b)+y⋅y+b-y)
Rewrite using the commutative property of multiplication.
-(b2-by-yb+y⋅y+b-y)
Multiply y by y.
-(b2-by-yb+y2+b-y)
-(b2-by-yb+y2+b-y)
Subtract yb from -by.
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Move y.
-(b2-by-by+y2+b-y)
Subtract by from -by.
-(b2-2by+y2+b-y)
-(b2-2by+y2+b-y)
-(b2-2by+y2+b-y)
Factor y-b-(y-b)^2

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