Suggested languages for you:

Americas

Europe

Q15.

Expert-verified
Found in: Page 469

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# Find each product.${\left(\mathbf{3}x-\mathbf{2}y\right)}^{2}$

$\mathbf{9}{x}^{2}-\mathbf{12}xy+\mathbf{4}{y}^{2}$

See the step by step solution

## Step 1. Write a pattern of square of a difference.

The square of $x-y$ is the square of x minus twice the product of x and y plus square of y, that is,

width="158" height="48" role="math" style="max-width: none; vertical-align: -25px;" localid="1647752100488" ${\left(x-y\right)}^{2}=\left(x-y\right)\left(x-y\right)\phantom{\rule{0ex}{0ex}}={x}^{2}-2xy+{y}^{2}$

## Step 2. Apply pattern of square of difference.

Apply the pattern of square of difference to the given expression.

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

## Step 3. Simplify.

Simplify the above obtained expression.

${3}^{2}{x}^{2}-2\cdot 3\cdot 2\cdot x\cdot y+{2}^{2}{y}^{2}=9{x}^{2}-12xy+4{y}^{2}$

Therefore, the product of ${\left(3x-2y\right)}^{2}$ is $9{x}^{2}-12xy+4{y}^{2}$.