Solve (3m-7)(3m+7)-2m(3/2m-1)

$$( 3 m - 7 ) ( 3 m + 7 ) - 2 m ( \frac { 3 } { 2 } m - 1 )$$

Evaluate

$$6m^{2}+2m-49$$

Solution Steps

Consider \left(3m-7\right)\left(3m+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3m\right)^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

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

$$3^{2}m^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9m^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

Calculate 7 to the power of 2 and get 49.

$$9m^{2}-49-2m\left(\frac{3}{2}m-1\right)$$

Use the distributive property to multiply -2m by \frac{3}{2}m-1.

$$9m^{2}-49-2m\times \frac{3}{2}m+2m$$

Multiply m and m to get m^{2}.

$$9m^{2}-49-2m^{2}\times \frac{3}{2}+2m$$

Multiply -2 times \frac{3}{2}.

$$9m^{2}-49-3m^{2}+2m$$

Combine 9m^{2} and -3m^{2} to get 6m^{2}.

$$6m^{2}-49+2m$$

Expand

$$6m^{2}+2m-49$$

Solution Steps

Consider \left(3m-7\right)\left(3m+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3m\right)^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

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

$$3^{2}m^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

Calculate 3 to the power of 2 and get 9.

$$9m^{2}-7^{2}-2m\left(\frac{3}{2}m-1\right)$$

Calculate 7 to the power of 2 and get 49.

$$9m^{2}-49-2m\left(\frac{3}{2}m-1\right)$$

Use the distributive property to multiply -2m by \frac{3}{2}m-1.

$$9m^{2}-49-2m\times \frac{3}{2}m+2m$$

Multiply m and m to get m^{2}.

$$9m^{2}-49-2m^{2}\times \frac{3}{2}+2m$$

Multiply -2 times \frac{3}{2}.

$$9m^{2}-49-3m^{2}+2m$$

Combine 9m^{2} and -3m^{2} to get 6m^{2}.

$$6m^{2}-49+2m$$