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Formula
Factorize the expression
Answer
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$$a ^ { 6 } - b ^ { 6 }$$
$\left ( a - b \right ) \left ( a + b \right ) \left ( a ^ { 2 } - a b + b ^ { 2 } \right ) \left ( a ^ { 2 } + a b + b ^ { 2 } \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 6 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 3 } } \right )$
$\left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 3 } } \right ) \left ( a ^ { 3 } - b ^ { 3 } \right )$
$ $ Use the factoring formula, $ a^{3} + b^{3} = \left(a+b\right)\left(a^{2}-ab + b^{2}\right)$
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right ) \left ( a ^ { 3 } - b ^ { 3 } \right )$
$\left ( a + b \right ) \left ( a ^ { 2 } - a b + b ^ { 2 } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 3 } } \right )$
$ $ Use the factoring formula, $ a^{3}-b^{3} = \left(a-b\right)\left(a^{2} + ab + b^{2}\right)$
$\left ( a + b \right ) \left ( a ^ { 2 } - a b + b ^ { 2 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right )$
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \right )$
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