Question
Factor polynomial $$ 256h^{4}-625k^{4} $$
Answer
$$ 256h^{4}-625k^{4} = (16h^{2}+25k^{2})(4h+5k)(4h-5k) $$
Explanation
Step 1 :
Rewrite $ 256h^4-625k^4 $ as:
$$ \color{blue}{ 256h^4-625k^4 = (16h^2)^2 - (25k^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 16h^2 $ and $ II = 25k^2 $ , we have:
$$ 256h^4-625k^4 = (16h^2)^2 - (25k^2)^2 = ( 16h^2-25k^2 ) ( 16h^2+25k^2 ) $$Step 2 :
Rewrite $ 16h^2-25k^2 $ as:
$$ \color{blue}{ 16h^2-25k^2 = (4h)^2 - (5k)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 4h $ and $ II = 5k $ , we have:
$$ 16h^2-25k^2 = (4h)^2 - (5k)^2 = ( 4h-5k ) ( 4h+5k ) $$This page was created using
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