Question

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

Answer 1

We can use:

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

$(5z^2+3z+2)^2\\\\=(5z^2)^2+(3z)^2+2^2+2(5z^2)(3z)+2(5z^2)(2)+2(3z)(2)\\\\=5^2(z^2)^2+3^2z^2+4+30z^{2+1}+20z^2+12z\\\\=25z^4+9z^2+4+30z^3+20z^2+12z\\\\=25z^4+30z^3+29z^2+12z+4\to d)$

$\text{Answer:}\ d)\ 25z^4+30z^3+29z^2+12z+4$

$\text{Used:}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}$