How do you find the product #(5g+2h)^3#?

1 Answer

Answer:

#255g^3+150g^2h+60gh^2+8h^3#

Explanation:

We can work this in a couple of ways.

  • One way is to manually multiply the terms the "long way". I'll decline to work this problem that way here.

  • The other way is to use Binomial Expansion. That's the way I'll work the problem.

The general form for binomial expansion is:

#(a+b)^n=(C_(n,0))a^nb^0+(C_(n,1))a^(n-1)b^1+...+(C_(n,n))a^0b^n#

In this case, #a=5g, b=2h, n=3#

#(5g+2h)^3#

#=(C_(3,0))(5g)^3(2h)^0+(C_(3,1))(5g)^2(2h)^1+(C_(3,2))(5g)^1(2h)^2+(C_(3,3))(5g)^0(2h)^3#

#=(1)(255)(g^3)(1)+(3)(25)(g^2)(2h)+(3)(5g)(4)(h^2)+(1)(1)(8)(h^3)#

#=255g^3+150g^2h+60gh^2+8h^3#