Question
Evaluate: $(5 m-2 n)(5 m+2 n)\left(25 m^2+4 n^2\right)$
✓
Answer
$(5m - 2n)(5m + 2n)(25m^2 + 4n^2)$
$= {5m (5m + 2n) - 2n(5m + 2n)} (25m^2 + 4n^2)$
$= (25m^2 + 10mn - 10mn - 4n^2)(25m^2 + 4n^2)$
$= (25m^2 - 4n^2)(25m^2 + 4n^2)$
$= 25m^2 (25m^2 + 4n^2) - 4n^2 (25m^2 + 4n^2)$
$= 625m^4 + 100m^2n^2 - 100m^2n^2 - 16n^4$
$= 625m^4 - 16n^4$
$= {5m (5m + 2n) - 2n(5m + 2n)} (25m^2 + 4n^2)$
$= (25m^2 + 10mn - 10mn - 4n^2)(25m^2 + 4n^2)$
$= (25m^2 - 4n^2)(25m^2 + 4n^2)$
$= 25m^2 (25m^2 + 4n^2) - 4n^2 (25m^2 + 4n^2)$
$= 625m^4 + 100m^2n^2 - 100m^2n^2 - 16n^4$
$= 625m^4 - 16n^4$
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