Question 72750
I'm assuming you want to distribute the w right? Well if you do, you will want to multiply w by every term inside the parenthesis.
{{{w(2w^3-9w^2)}}}Start with given expression
{{{w*2w^3-w*9w^2)}}}Distribute the w. This means that the w is multiplied by 2w^3 and 9w^2
{{{2w^4-9w^3}}}Simplify the expression. When multiplying 2 variables with exponents you add the exponents (for example {{{x^3*x^2=x^(2+3)=x^5}}})
<p>
If that didn't make any sense, or you just are having a hard time understanding distribution, make a simpler problem. For instance try looking at
{{{x(x+5)}}}
{{{x(x+5)}}}Distribute the x among x and 5
{{{x*x+x*5}}}Simplify
{{{x^2+5x}}}
To help even further, lets put some numbers into this expression. Let x=2
{{{highlight(2)*(highlight(2)+5)}}}place x=2 into each x
{{{2*2+2*5}}}
{{{4+10}}}
{{{14}}}
It turns out that if we add the values inside the parenthesis and then multiply, we will get the same answer
{{{2*(2+5)}}}
{{{2*(7)}}}
{{{14}}}Which shows that {{{2*(2+5)=2*2+2*5}}} is true. The reason why we have to distribute in this problem is because we don't know what w is. w could be anything, so we cannot add it to a known value (there's no way to do it). So we distribute the w to simplify the problem, and since there are no further instructions, we'll leave it at
{{{2w^4-9w^3}}} Hope this helps. Throughout this problem, I'm assuming that distribution is giving you trouble and I hope I'm correct.