Question 544058
Given to multiply:
.
{{{(5z+2)(z^2+3z+2)}}}
.
First multiply the 5z in the first set of parentheses by each of the three terms in the second set of parentheses as follows:
.
{{{5z*z^2 = 5z^3}}} then
{{{5z*3z = 15z^2}}} and finally
{{{5z*2 = 10z}}}
.
Next multiply the 2 in the first set of parentheses by each of the three terms in the second set of parentheses as follows:
.
{{{2*z^2 = 2z^2}}} then
{{{2*3z = 6z}}} and finally
{{{2*2 = 4}}}
.
Add all the answers together:
.
{{{5z^3 + 15z^2 + 10z + 2z^2 + 6z +4}}}
.
collect all the terms that have the same power of z:
.
{{{5z^3 + (15z^2 + 2z^2)+ (10z + 6z)+4}}}
.
combine the terms having the same power of z (in the two sets of parentheses) and you get:
.
{{{5z^3 + 17z^2 + 16z + 4}}}
.
And that's the answer.
.
Hope this helps you to understand the problem better.
.