The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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