Solve (7m+4)^2-(2m-5)^2

$$( 7 m + 4 ) ^ { 2 } - ( 2 m - 5 ) ^ { 2 }$$

Evaluate

$$\left(9m-1\right)\left(5m+9\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7m+4\right)^{2}.

$$49m^{2}+56m+16-\left(2m-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-5\right)^{2}.

$$49m^{2}+56m+16-\left(4m^{2}-20m+25\right)$$

To find the opposite of 4m^{2}-20m+25, find the opposite of each term.

$$49m^{2}+56m+16-4m^{2}+20m-25$$

Combine 49m^{2} and -4m^{2} to get 45m^{2}.

$$45m^{2}+56m+16+20m-25$$

Combine 56m and 20m to get 76m.

$$45m^{2}+76m+16-25$$

Subtract 25 from 16 to get -9.

$$45m^{2}+76m-9$$

Expand

$$45m^{2}+76m-9$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7m+4\right)^{2}.

$$49m^{2}+56m+16-\left(2m-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-5\right)^{2}.

$$49m^{2}+56m+16-\left(4m^{2}-20m+25\right)$$

To find the opposite of 4m^{2}-20m+25, find the opposite of each term.

$$49m^{2}+56m+16-4m^{2}+20m-25$$

Combine 49m^{2} and -4m^{2} to get 45m^{2}.

$$45m^{2}+56m+16+20m-25$$

Combine 56m and 20m to get 76m.

$$45m^{2}+76m+16-25$$

Subtract 25 from 16 to get -9.

$$45m^{2}+76m-9$$