Find the product.

[tex]\[ 2y^2(3x + 5z) \][/tex]

A. [tex]\(5xy^2 + 7y^2z\)[/tex]
B. [tex]\(6xy^2 + 10y^2z^2\)[/tex]
C. [tex]\(6xy^2 + 10y^2z\)[/tex]



Answer :

Let's go through the problem step by step and find the product.

We are given the expression:
[tex]\[ 2y^2(3x + 5z) \][/tex]

To solve this, we need to distribute [tex]\(2y^2\)[/tex] to each term inside the parentheses.

1. Distribute [tex]\(2y^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[ 2y^2 \cdot 3x = 6xy^2 \][/tex]

2. Distribute [tex]\(2y^2\)[/tex] to [tex]\(5z\)[/tex]:
[tex]\[ 2y^2 \cdot 5z = 10y^2z \][/tex]

Putting these two results together, we get:
[tex]\[ 2y^2(3x + 5z) = 6xy^2 + 10y^2z \][/tex]

Now, let's compare this result with the given possible answers:

1. [tex]\(5xy^2 + 7y^2z\)[/tex]
2. [tex]\(6xy^2 + 10y^2z^2\)[/tex]
3. [tex]\(6xy^2 + 10y^2z\)[/tex]

From our calculations, we see that the product [tex]\(2y^2(3x + 5z)\)[/tex] simplifies to [tex]\(6xy^2 + 10y^2z\)[/tex].

Therefore, the correct answer is:
[tex]\[ 6xy^2 + 10y^2z \][/tex]