Can someone explain how to do part b?

3

Step-by-step explanation:

4(a) The first 3 terms are:

₅C₀ (3)⁵ (bx)⁰ = 1 × 3⁵ × 1 = 243

₅C₁ (3)⁴ (bx)¹ = 5 × 3⁴ × bx = 405b x

₅C₂ (3)³ (bx)² = 10 × 3³ × (bx)² = 270b² x²

4(b) The coefficient of x² (the third term) is twice the coefficient of x (the second term).

270b² = 2 (405 b)

270b² = 810b

270b = 810

b = 3

3

Step-by-step explanation:

Term in x²: 270b²x²

Coefficient: 270b²

Term in x: 405bx

Coefficient: 405b

270b² = 2(405b)

270b² - 810b = 0

270b(b - 3) = 0

b = 0, 3

Since b is non-zero,

b = 3

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: