Q15. - Algebra 1

Question

Find each product.

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

Step-by-Step Solution

Answer

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

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" style="max-width: none; vertical-align: -25px;" $$\begin{gathered} {\left(x-y\right)}^2=\left(x-y\right)\left(x-y\right) \\ =x^2-2xy+y^2 \end{gathered}$$

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.

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

 

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