For a binomial expansion with exponent 5, the general equation is as follows
(x + y)⁵ = x⁵ + 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴ + y⁵
when expanded from left to right the powers of x decrease from 5 to 0 and powers of y increase from 0 to 5
substitute x =2x and y = 5
(2x + 5)⁵ = (2x)⁵ + 5(2x)⁴5 + 10(2x)³5² + 10(2x)²5³ + 5(2x)5⁴ + 5⁵
<span>= 32x⁵ + 400x⁴ + 2000x³ + 5000x² + 6250x + 3125
</span>we use the pascals triangle to find the coefficient
we can use the binomial theorem to find the 4th term as well
exponent - 5
term - 4
5!/ (5-4)!4! * (2x)⁴5⁵⁻⁴
=120/24 *16x⁴*5
=400x⁴
Answer:
30:24
Step-by-step explanation:
5 + 4 = 9
Divide 54 by 9
Then Multiply by 6.
Hope it helped.
Answer:
a₄₂ = 107
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂₇ = 66 , then
a₁ + 26d = 66 , that is
- 12 + 26d = 66 ( add 12 to both sides )
26d = 78 ( divide both sides by 26 )
d = 3
Then
a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111
Answer: barely can see anything..
Step-by-step explanation:
