Question

Factor by groupingd)z² + 2z + 3zy + 6y​

Answer 1

Ответ:

(z+2)(z+3y)

Объяснение:

z(z+2)+3y(z+2)

(z+2)(z+3y)

Answer 2

To factor by grouping, we need to group the terms in pairs and then look for common factors within each group. Let's factor the expression $z^2 + 2z + 3zy + 6y$ step by step:

Step 1: Group the terms in pairs. $z^2 + 2z$ and $3zy + 6y$

Step 2: Look for common factors within each group. In the first group $z^2 + 2z$, we can factor out $z$: $z(z + 2)$

In the second group $3zy + 6y$, we can factor out $3y$: $3y(z + 2)$

Step 3: Now, notice that both groups have a common factor of $(z + 2)$: $z(z + 2) + 3y(z + 2)$

Step 4: Factor out $(z + 2)$ from both terms: $(z + 2)(z + 3y)$

So, the factored form of the expression $z^2 + 2z + 3zy + 6y$ is $(z + 2)(z + 3y)$.