Solve [(m-53)-(m-471]^2+2(m-5)(m+4))

$$[ ( m - 53 ) - ( m - 471 ] ^ { 2 } + 2 ( m - 5 ) ( m + 4 ) )$$

Evaluate

$$m^{2}+941m-221934$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-471\right)^{2}.

$$m-53-\left(m^{2}-942m+221841\right)+2\left(m-5\right)\left(m+4\right)$$

To find the opposite of m^{2}-942m+221841, find the opposite of each term.

$$m-53-m^{2}+942m-221841+2\left(m-5\right)\left(m+4\right)$$

Combine m and 942m to get 943m.

$$943m-53-m^{2}-221841+2\left(m-5\right)\left(m+4\right)$$

Subtract 221841 from -53 to get -221894.

$$943m-221894-m^{2}+2\left(m-5\right)\left(m+4\right)$$

Use the distributive property to multiply 2 by m-5.

$$943m-221894-m^{2}+\left(2m-10\right)\left(m+4\right)$$

Use the distributive property to multiply 2m-10 by m+4 and combine like terms.

$$943m-221894-m^{2}+2m^{2}-2m-40$$

Combine -m^{2} and 2m^{2} to get m^{2}.

$$943m-221894+m^{2}-2m-40$$

Combine 943m and -2m to get 941m.

$$941m-221894+m^{2}-40$$

Subtract 40 from -221894 to get -221934.

$$941m-221934+m^{2}$$

Expand

$$m^{2}+941m-221934$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-471\right)^{2}.

$$m-53-\left(m^{2}-942m+221841\right)+2\left(m-5\right)\left(m+4\right)$$

To find the opposite of m^{2}-942m+221841, find the opposite of each term.

$$m-53-m^{2}+942m-221841+2\left(m-5\right)\left(m+4\right)$$

Combine m and 942m to get 943m.

$$943m-53-m^{2}-221841+2\left(m-5\right)\left(m+4\right)$$

Subtract 221841 from -53 to get -221894.

$$943m-221894-m^{2}+2\left(m-5\right)\left(m+4\right)$$

Use the distributive property to multiply 2 by m-5.

$$943m-221894-m^{2}+\left(2m-10\right)\left(m+4\right)$$

Use the distributive property to multiply 2m-10 by m+4 and combine like terms.

$$943m-221894-m^{2}+2m^{2}-2m-40$$

Combine -m^{2} and 2m^{2} to get m^{2}.

$$943m-221894+m^{2}-2m-40$$

Combine 943m and -2m to get 941m.

$$941m-221894+m^{2}-40$$

Subtract 40 from -221894 to get -221934.

$$941m-221934+m^{2}$$