Question

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

Answer 1

Answer:

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

Step-by-step 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

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

Answer 2

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