# How do you multiply 4xy^2(3x^2-5xy+6y^2)?

Nov 13, 2017

$12 {x}^{3} {y}^{2} - 20 {x}^{2} {y}^{3} + 24 {x}^{2} {y}^{4}$

#### Explanation:

First, we need to know that
${a}^{n} \cdot {a}^{m} = {a}^{n + m}$

For this question, we can simply expand the bracket.
$4 x {y}^{2} \left(3 {x}^{2} - 5 x y + 6 {y}^{2}\right)$

$= 3 {x}^{2} \cdot 4 x {y}^{2} - 5 x y \cdot 4 x {y}^{2} + 6 {y}^{2} \cdot 4 x {y}^{2}$

$= 3 \cdot 4 \cdot {x}^{2} \cdot x \cdot {y}^{2} - 5 \cdot 4 \cdot x \cdot x \cdot y \cdot {y}^{2} + 6 \cdot 4 \cdot {x}^{2} \cdot {y}^{2} \cdot {y}^{2}$

$= 12 {x}^{2 + 1} {y}^{2} - 20 {x}^{1 + 1} {y}^{1 + 2} + 24 {x}^{2} {y}^{2 + 2}$

$= 12 {x}^{3} {y}^{2} - 20 {x}^{2} {y}^{3} + 24 {x}^{2} {y}^{4}$

Here is the answer :)