Solve {l}{(2x-3y)^2}{-6(2x-3y)}{+9}

$$\left. \begin{array} { l } { ( 2 x - 3 y ) ^ { 2 } } \\ { - 6 ( 2 x - 3 y ) } \\ { + 9 } \end{array} \right.$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-6\left(2x-3y\right)+9$$

Use the distributive property to multiply -6 by 2x-3y.

$$4x^{2}-12xy+9y^{2}-12x+18y+9$$

Expand

$$4x^{2}-12xy-12x+9y^{2}+18y+9$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-6\left(2x-3y\right)+9$$

Use the distributive property to multiply -6 by 2x-3y.

$$4x^{2}-12xy+9y^{2}-12x+18y+9$$