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

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Answer 1 · 2017-12-26T06:21:31

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

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, $a=5g, b=2h, n=3$

$(5g+2h)^3$

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

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

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

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