Multiply the polynomials: $- 4 u^{2} v (4 u^{2} v^{2} + 2 v^{2} - u^{2} + 4)$

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Solution

$- 4 u^{2} v (4 u^{2} v^{2} + 2 v^{2} - u^{2} + 4)$
Multiply the coefficients and add the exponents of the variable.
$=$ $- 4 u^{2} v .4 u^{2} v^{2} + (- 4 u^{2} v) .2 v^{2} + (- 4 u^{2} v) . (- u^{2}) + (- 4 u^{2} v) .4$
$=$ $- 16 u^{4} v^{3} - 8 u^{2} v^{3} + 4 u^{4} v - 16 u^{2} v$
$=$ $4 u^{4} v - 16 u^{4} v^{3} - 8 u^{2} v^{3} - 16 u^{2} v$

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