what expression is equivalent to $(5z^{2}+3z + 2)^{2}$?\n$5z^{4}+3z^{2}+4$\n$5z^{4}+9z^{2}+4$\n$25z^{4}+30z^{…

Explanation:

Step1: Expand using formula $(a + b + c)^2=a^{2}+b^{2}+c^{2}+2ab + 2ac+2bc$

Here $a = 5z^{2}$, $b = 3z$, $c = 2$. So $(5z^{2}+3z + 2)^{2}=(5z^{2})^{2}+(3z)^{2}+2^{2}+2\times(5z^{2})\times(3z)+2\times(5z^{2})\times2+2\times(3z)\times2$.

Step2: Calculate each term

$(5z^{2})^{2}=25z^{4}$, $(3z)^{2}=9z^{2}$, $2^{2}=4$, $2\times(5z^{2})\times(3z)=30z^{3}$, $2\times(5z^{2})\times2 = 20z^{2}$, $2\times(3z)\times2=12z$.

Step3: Combine like - terms

$25z^{4}+9z^{2}+4 + 30z^{3}+20z^{2}+12z=25z^{4}+30z^{3}+(9z^{2}+20z^{2})+12z + 4=25z^{4}+30z^{3}+29z^{2}+12z + 4$.

Answer:

$25z^{4}+30z^{3}+29z^{2}+12z + 4$