How do you multiply (3x^2 + 2y)(7x^2 + 3y)?

Jul 26, 2016

$\left(3 {x}^{2} + 2 y\right) \left(7 {x}^{2} + 3 y\right)$

$21 {x}^{4} + 9 {x}^{2} y + 14 {x}^{2} y + 6 {y}^{2}$

$21 {x}^{4} + 23 {x}^{2} y + 6 y$

Explanation:

Step 1
I multiplied
$3 {x}^{2}$ with $7 {x}^{2}$
Step 2
I multiplied $3 {x}^{2}$ with $3 y$.
So far we have $21 {x}^{4} + 9 {x}^{2} y$
Step 3
I multiplied $2 y$ with $7 {x}^{2}$
Step 4
I multiplied $2 y$ with $3 y$.
We have $14 {x}^{2} y + 6 {y}^{2}$
Step 5
In total, we have $21 {x}^{4} + 9 {x}^{2} y + 14 {x}^{2} y + 6 {y}^{2}$
Step 6
We combine like terms. You will see the only like terms are $9 {x}^{2} y + 14 {x}^{2} y$ Those are the only terms we combine.
Final Step
We combine everything
SO our answer is $21 {x}^{4} + 23 {x}^{2} y + 6 {y}^{2}$