Answer:
- 23
Step-by-step explanation:
We could do this the long way and expand the whole product or note that the
terms arise from the product of the a³ and a terms and the product of the a² and a² terms, that is
4a³ × 3a = 12
+ 5a² × - 7a² = - 35
Summing gives
12
- 35
= - 23
with coefficient - 23
The cube root values and a graph of them are shown in the attachment.
_____
The cube root of a negative number is negative. These all have exact (rational) cube roots.
∑ from 1 to infinity of 12(3/5)^(i - 1)
Since the common ratio is less than 1, the series is convegent. [i.e. 3/5 < 1]
Sum to infinity of a geometric series is given by a/(1 - r); where a is the first term, and r is the common ratio.
Sum = 12/(1 - 3/5) = 12/(2/5) = 30.
Left is plus right is negative -11-(-15)=4 so you know 4 to the left