Use the binomial theorem to expand (2a+2b)^6

The answer to your question is below

Step-by-step explanation:

Pascal´s triangle

                             1   6    15   20   15   6   1

Then

(2a + 2b)⁶ = (2a)⁶ + 6(2a)⁵(2b) + 15(2a)⁴(2b)² + 20(2a)³(2b)³ + 15(2a)²(2b)⁴

                   6(2a)(2b)⁵ + (2b)⁶

Simplifying

               =  64a⁶ + 6(32a⁵)(2b) + 15(16a⁴)(4b²) + 20(8a³)(8b³) + 15(4a²)(16b⁴)

                   6(2a)(32b⁵) + 64b⁶

              = 64a⁶ + 384a⁵b + 960a⁴b² + 1280a³b³ + 960a²b⁴ + 384ab⁵ + 64b⁶

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!