Question

Which expression is equivalent to (5z^2+3z+2)^2

Answer 1

Which expression is equivalent to (5z^2+3z+2)^2

Answer 2

`25z^(4) +30z^(3) +29z^(2) +12z+4`

Explanation:

The trinomial is squared, so it can be solved with the following notable product

`(a+b+c)^(2)  = a^(2) +b^(2) +c^(2) +2ab+2ac+2bc`

If we substitute the indicated values

`a=5z^(2) ;    b=3z;     c=2`

Tendremos lo siguiente

`(5z^(2) +3z+2)^(2) = (5z^(2) )^(2) +(3z)^(2) +2^(2) +2(5z^(2) )(3z)+2(5z^(2) )(2)+2(3z)(2)`

performing indicated operations

`25z^(4) +9z^(2) +4+30z^(3) +20z^(2) +12z`

accommodating terms

`25z^(4) +30z^(3) +9z^(2) +20z^(2) +12z+4`

reducing terms

`25z^(4) +30z^(3) +29z^(2) +12z+4`