Solve left(a-1right)^2-left(m-2right)^2

$${ \left(a-1 \right) }^{ 2 } - { \left(m-2 \right) }^{ 2 }$$

Evaluate

$$\left(m+a-3\right)\left(1+a-m\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$a^{2}-2a+1-\left(m-2\right)^{2}$$

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

$$a^{2}-2a+1-\left(m^{2}-4m+4\right)$$

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

$$a^{2}-2a+1-m^{2}+4m-4$$

Subtract 4 from 1 to get -3.

$$a^{2}-2a-3-m^{2}+4m$$

Expand

$$-m^{2}+4m+a^{2}-2a-3$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$a^{2}-2a+1-\left(m-2\right)^{2}$$

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

$$a^{2}-2a+1-\left(m^{2}-4m+4\right)$$

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

$$a^{2}-2a+1-m^{2}+4m-4$$

Subtract 4 from 1 to get -3.

$$a^{2}-2a-3-m^{2}+4m$$