Solve (3m-1)^2-(2m-3)^2

$$( 3 m - 1 ) ^ { 2 } - ( 2 m - 3 ) ^ { 2 }$$

Evaluate

$$\left(5m-4\right)\left(m+2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3m-1\right)^{2}.

$$9m^{2}-6m+1-\left(2m-3\right)^{2}$$

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

$$9m^{2}-6m+1-\left(4m^{2}-12m+9\right)$$

To find the opposite of 4m^{2}-12m+9, find the opposite of each term.

$$9m^{2}-6m+1-4m^{2}+12m-9$$

Combine 9m^{2} and -4m^{2} to get 5m^{2}.

$$5m^{2}-6m+1+12m-9$$

Combine -6m and 12m to get 6m.

$$5m^{2}+6m+1-9$$

Subtract 9 from 1 to get -8.

$$5m^{2}+6m-8$$

Expand

$$5m^{2}+6m-8$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3m-1\right)^{2}.

$$9m^{2}-6m+1-\left(2m-3\right)^{2}$$

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

$$9m^{2}-6m+1-\left(4m^{2}-12m+9\right)$$

To find the opposite of 4m^{2}-12m+9, find the opposite of each term.

$$9m^{2}-6m+1-4m^{2}+12m-9$$

Combine 9m^{2} and -4m^{2} to get 5m^{2}.

$$5m^{2}-6m+1+12m-9$$

Combine -6m and 12m to get 6m.

$$5m^{2}+6m+1-9$$

Subtract 9 from 1 to get -8.

$$5m^{2}+6m-8$$