Answer :
[tex]6{y}^{4} {z}^{2} + 12 {y}^{3} {z}^{2}-3 {y}^{3} {z}+3 {y}^{2} {z}^{2}[/tex]
Step-by-step explanation :
To find the product of
[tex]3 {y}^{2} z(2 {y}^{2} z + 4yz - y + z)[/tex]
First we expand the bracket ,
it implies that, we use the expression outside the bracket to multiply individual expressions inside the bracket.
Hence
[tex] 3 {y}^{2} z(2 {y}^{2} z + 4yz - y + z)[/tex]
[tex] = 3 {y}^{2} z(2 {y}^{2} z) + 3 {y}^{2} z(4yz) - 3 {y}^{2} z(y )+3 {y}^{2} z( z)[/tex]
we now apply the law of indices
[tex] {a}^{m} \times {a}^{n} = {a}^{m+n}[/tex]
meaning, when you are multiplying two expressions with the same bases , repeat one of the bases and add the exponents.
Then, simplify to obtain
[tex] = 6{y}^{4} {z}^{2} + 12 {y}^{3} {z}^{2}-3{y}^{3} {z}+3 {y}^{2} {z}^{2}[/tex]
