Maths ALevel Homework help

Hi, I’m super confused how to do this question on my homework, could someone explain it to me?
In the expansion of (a + 3x)⁸, the coefficent of x² is 32/27 times the coefficent of x⁵. What is the value of a?

Reply 1

the bear

so expand from low powers of x to higher powers as far as the x⁵ term.

now compare the coefficients of the x² and x⁵ terms.

Reply 2

lissishannyn

Original post by the bear

so expand from low powers of x to higher powers as far as the x⁵ term.

now compare the coefficients of the x² and x⁵ terms.

we have to do it using binomial theorem and with some formula using factorials and i really don't get it?

Reply 3

Melvin Guna

Original post by lissishannyn

we have to do it using binomial theorem and with some formula using factorials and i really don't get it?

You don't need to do the full binomial expansion - just look for the terms with the power you need and calculate the coefficients based on the following formula in red

(edited 3 years ago)

Reply 4

the bear

so for instance the x³ term....

8C3 * a⁵ * ( 3x )³....

which is 56*a⁵*27*x³

Reply 5

lissishannyn

Original post by Melvin Guna

You don't need to do the full binomial expansion - just look for the terms with the power you need and calculate the coefficients based on the following formula in red

thank you so much ive got it now :smile: