Question

How do you multiply out `(5z^2+3z+2)^2`?

Answer 1

=`25z^4+30x^3+29z^2+12z+4`

Explanation:

Note that there are 3 terms inside the bracket. DO NOT make the common mistake of simply squaring each term!!

Squaring means, multiply by itself.
`(5z^2 +3z +2)^2`

=`(color(red)(5z^2) color(blue)(+3z) color(orange)(+2))xx(5z^2 +3z +2)`

Each term in the first bracket must be multiplied by each term in the second bracket. This will give us 9 terms which we can then simplify.

=`color(red)(25z^4 +15z^3+10z^2) color(blue)(+15z^3+9z^2 +6z)color(orange)(+10z^2+6z +4)`

Collect like terms and arrange them in descending powers of z.

`color(purple)(25z^4) +color(green)(15z^3)+color(magenta)(10z^2)color(green)(+15z^3)+color(magenta)(9z^2) color(yellow)(+6z)+color(magenta)(10z^2)+color(yellow)(6z) +4`

=`25z^4+30x^3+29z^2+12z+4`