Solve -9+24(m-n)-16(m-n)^2

$$- 9 + 24 ( m - n ) - 16 ( m - n ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 24 by m-n.

$$-9+24m-24n-16\left(m-n\right)^{2}$$

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

$$-9+24m-24n-16\left(m^{2}-2mn+n^{2}\right)$$

Use the distributive property to multiply -16 by m^{2}-2mn+n^{2}.

$$-9+24m-24n-16m^{2}+32mn-16n^{2}$$

Expand

$$-16m^{2}+32mn+24m-16n^{2}-24n-9$$

Solution Steps

Use the distributive property to multiply 24 by m-n.

$$-9+24m-24n-16\left(m-n\right)^{2}$$

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

$$-9+24m-24n-16\left(m^{2}-2mn+n^{2}\right)$$

Use the distributive property to multiply -16 by m^{2}-2mn+n^{2}.

$$-9+24m-24n-16m^{2}+32mn-16n^{2}$$