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Expand the expression
Answer
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Factorize the expression
Answer
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$\left( x-1 \right) x ^{ 2 } - \left( x-1 \right) y ^{ 2 }$
$x ^ { 3 } - x ^ { 2 } - x y ^ { 2 } + y ^ { 2 }$
Organize polynomials
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - \left ( x - 1 \right ) y ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - \left ( x - 1 \right ) y ^ { 2 }$
$x ^ { 3 } - x ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) y ^ { 2 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$x ^ { 3 } - x ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) y ^ { 2 }$
$x ^ { 3 } - x ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the expression with the distributive law $ $
$x ^ { 3 } - x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\left ( x - 1 \right ) \left ( x - y \right ) \left ( x + y \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right )$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
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