Solve 4Lm-(3L+2m)^2

$$4 L m - ( 3 L + 2 m ) ^ { 2 }$$

Evaluate

$$-\left(2m+3L\right)^{2}+4Lm$$

Solution Steps

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

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

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

$$4Lm-9L^{2}-12Lm-4m^{2}$$

Combine 4Lm and -12Lm to get -8Lm.

$$-8Lm-9L^{2}-4m^{2}$$

Expand

$$-4m^{2}-8Lm-9L^{2}$$

Solution Steps

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

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

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

$$4Lm-9L^{2}-12Lm-4m^{2}$$

Combine 4Lm and -12Lm to get -8Lm.

$$-8Lm-9L^{2}-4m^{2}$$