Solve {l}{(3m-2n)(3m+2n)}{+m(3-m)}

$$\left. \begin{array} { l } { ( 3 m - 2 n ) ( 3 m + 2 n ) } \\ { + m ( 3 - m ) } \end{array} \right.$$

Evaluate

$$8m^{2}+3m-4n^{2}$$

Solution Steps

Consider \left(3m-2n\right)\left(3m+2n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3m\right)^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Expand \left(3m\right)^{2}.

$$3^{2}m^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Calculate 3 to the power of 2 and get 9.

$$9m^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Expand \left(2n\right)^{2}.

$$9m^{2}-2^{2}n^{2}+m\left(3-m\right)$$

Calculate 2 to the power of 2 and get 4.

$$9m^{2}-4n^{2}+m\left(3-m\right)$$

Use the distributive property to multiply m by 3-m.

$$9m^{2}-4n^{2}+3m-m^{2}$$

Combine 9m^{2} and -m^{2} to get 8m^{2}.

$$8m^{2}-4n^{2}+3m$$

Expand

$$8m^{2}+3m-4n^{2}$$

Solution Steps

Consider \left(3m-2n\right)\left(3m+2n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3m\right)^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Expand \left(3m\right)^{2}.

$$3^{2}m^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Calculate 3 to the power of 2 and get 9.

$$9m^{2}-\left(2n\right)^{2}+m\left(3-m\right)$$

Expand \left(2n\right)^{2}.

$$9m^{2}-2^{2}n^{2}+m\left(3-m\right)$$

Calculate 2 to the power of 2 and get 4.

$$9m^{2}-4n^{2}+m\left(3-m\right)$$

Use the distributive property to multiply m by 3-m.

$$9m^{2}-4n^{2}+3m-m^{2}$$

Combine 9m^{2} and -m^{2} to get 8m^{2}.

$$8m^{2}-4n^{2}+3m$$