Consider the given polynomial, a^7+ab^6 #10; #10; #160; #10;a^7+ab^6=a( a^6 b^6)=a[ ( #10;a^3)^2 ( b^3)^2] #10; #10; #160; #10;=a[ ...

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(x±a)(x±b) = x²±(a+b)x+ab.

Factorize: ...

Question

Factorize: $a^{7} + a b^{6}$

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Solution

Consider the given polynomial, $a^{7} + a b^{6}$

$a^{7} + a b^{6} = a (a^{6} - b^{6}) = a [{(a^{3})}^{2} - {(b^{3})}^{2}]$

$= a [(a^{3} - b^{3}) (a^{3} + b^{3})] = a [(a - b) (a^{2} + b^{2} + a b) (a + b) (a^{2} + b^{2} - a b)]$

$= a (a - b) (a^{2} + b^{2} + a b) (a + b) (a^{2} + b^{2} - a b)$

This is the required factor .

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