Question

factorise x^6 - y^6 by using suitable identiy​

Answer 1

Step-by-step explanation:

Identity used

a^2–2ab+a^2

Your question,

x^6 – y^6

=(x^6)^2 – 2(x^6×y^6) + (y^6)^2

=x^12 – 2x^6y^6 + y^12

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Answer 2

Question

• factorise x^6 - y^6 by using suitable identiy

Answer

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⟼1) $\small\fbox\pink{(a)²-(b)²=(a+b)(a-b)}$

⟼2) $\small\fbox\pink{a³-b³=(a-b)(a²+b²+ab}$

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By using the first identity,we get as

$\tt\: {x}^{6} - {y}^{6} = ( {x}^{3} ) {}^{2} - ( {y}^{3} ) {}^{2}$

$\tt\: = ( {x}^{3} - {y}^{3} ) \: ( {x}^{3} + {y}^{3} )$

Now,

by using the second identity, we get as

$\tt\:(x - y)( {x}^{2} + xy + {y}^{2} )(x + y)( {x}^{2} - xy + y {}^{2} )$

$\tt\: = (x - y)(x + y)( {x}^{2} + xy + {y}^{2} )( {x}^{2} - xy + {y}^{2} )$

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Hence, the factors are

$\tt\: = (x - y)(x + y)( {x}^{2} + xy + {y}^{2} )( {x}^{2} - xy + {y}^{2} )$

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Answer 3

Question

• factorise x^6 - y^6 by using suitable identiy

Answer

______________________________________

⟼1) $\small\fbox\pink{(a)²-(b)²=(a+b)(a-b)}$

⟼2) $\small\fbox\pink{a³-b³=(a-b)(a²+b²+ab}$

______________________________________

By using the first identity,we get as

$\tt\: {x}^{6} - {y}^{6} = ( {x}^{3} ) {}^{2} - ( {y}^{3} ) {}^{2}$

$\tt\: = ( {x}^{3} - {y}^{3} ) \: ( {x}^{3} + {y}^{3} )$

Now,

by using the second identity, we get as

$\tt\:(x - y)( {x}^{2} + xy + {y}^{2} )(x + y)( {x}^{2} - xy + y {}^{2} )$

$\tt\: = (x - y)(x + y)( {x}^{2} + xy + {y}^{2} )( {x}^{2} - xy + {y}^{2} )$

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Hence, the factors are

$\tt\: = (x - y)(x + y)( {x}^{2} + xy + {y}^{2} )( {x}^{2} - xy + {y}^{2} )$

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