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Expand the expression
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Factorize the expression
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$\left( x+a \right) ^{ 2 } -2 \left( x+a \right) \left( y+a \right) + \left( y+a \right) ^{ 2 }$
$x ^ { 2 } - 2 x y + y ^ { 2 }$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) ^ { \color{#FF6800}{ 2 } } - 2 \left ( x + a \right ) \left ( y + a \right ) + \left ( y + a \right ) ^ { 2 }$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ x } + \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } - 2 \left ( x + a \right ) \left ( y + a \right ) + \left ( y + a \right ) ^ { 2 }$
$x ^ { 2 } + 2 a x + a ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) \left ( y + a \right ) + \left ( y + a \right ) ^ { 2 }$
$ $ Use the law of distribution $ $
$x ^ { 2 } + 2 a x + a ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \left ( y + a \right ) + \left ( y + a \right ) ^ { 2 }$
$x ^ { 2 } + 2 a x + a ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) + \left ( y + a \right ) ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } + 2 a x + a ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } + \left ( y + a \right ) ^ { 2 }$
$x ^ { 2 } + 2 a x + a ^ { 2 } - 2 x y - 2 a x - 2 a y - 2 a ^ { 2 } + \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the binomial expression $ $
$x ^ { 2 } + 2 a x + a ^ { 2 } - 2 x y - 2 a x - 2 a y - 2 a ^ { 2 } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ y } + \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$x ^ { 2 } + \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \color{#FF6800}{ x } + \left ( a ^ { 2 } - 2 a ^ { 2 } + a ^ { 2 } \right ) - 2 x y + \left ( - 2 a + 2 a \right ) y + y ^ { 2 }$
$ $ Organize the mononomial expression $ $
$x ^ { 2 } + \color{#FF6800}{ 0 } + \left ( a ^ { 2 } - 2 a ^ { 2 } + a ^ { 2 } \right ) - 2 x y + \left ( - 2 a + 2 a \right ) y + y ^ { 2 }$
$x ^ { 2 } + 0 + \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \right ) - 2 x y + \left ( - 2 a + 2 a \right ) y + y ^ { 2 }$
$ $ Arrange the constant term $ $
$x ^ { 2 } + 0 + \color{#FF6800}{ 0 } - 2 x y + \left ( - 2 a + 2 a \right ) y + y ^ { 2 }$
$x ^ { 2 } + 0 + 0 - 2 x y + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \right ) \color{#FF6800}{ y } + y ^ { 2 }$
$ $ Organize the mononomial expression $ $
$x ^ { 2 } + 0 + 0 - 2 x y + \color{#FF6800}{ 0 } + y ^ { 2 }$
$x ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ 0 } \color{#FF6800}{ + } \color{#FF6800}{ 0 } - 2 x y \color{#FF6800}{ + } \color{#FF6800}{ 0 } + y ^ { 2 }$
$ $ 0 does not change when you add or subtract $ $
$x ^ { 2 } - 2 x y + y ^ { 2 }$
$\left ( x - y \right ) ^ { 2 }$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ a } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Use the factoring formula, $ a^{2}-2ab + b^{2} = \left(a-b\right)^{2}$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } }$
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