Question
Factor polynomial $$ a^{5}b^{4}+a^{8}b $$
Answer
$$ a^{5}b^{4}+a^{8}b = a^{5}b(b+a)(b^{2}-ab+a^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ a^5b } $:
$$ a^5b^4+a^8b = a^5b ( b^3+a^3 ) $$Step 2 :
To factor $ b^{3}+a^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = b $ and $ II = a $ , we have:
$$ b^{3}+a^{3} = ( b+a ) ( b^{2}-ab+a^{2} ) $$This page was created using
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