Q.218. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

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

Step-by-Step Solution

Answer

The solution is $9x^2-6xy+y^2$.

Step 1. Given information.

The given expression is ${\left(3x-y\right)}^2$.

Step 2. Simplify the given expression by using the binomial squares pattern a - b 2 = a 2 - 2 a b + b 2 .

Solve it as follows:

$$\begin{gathered} {\left(3x-y\right)}^2={\left(3x\right)}^2-2\times 3x\times y+{\left(y\right)}^2 \\ \Rightarrow 9x^2-6xy+y^2 \end{gathered}$$

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are $9x^2-6xy+y^2$.