Expand (m - 2)^2.

Step-by-step solution

1. 1

   Use the square-of-a-difference identity, not term-by-term squaring. The formula is

   $(a-b)^{2}=a^{2}-2ab+b^{2}$

   There are three terms in the result, not two. Writing $(m-2)^{2}=m^{2}-4$ is the single most common error — it drops the middle term entirely and mistakes the pattern for a difference of squares.

2. 2

   Match the pattern. Here $a=m$ and $b=2$, so:

   $a^{2}=m^{2},\qquad2ab=2\cdot m\cdot2=4m,\qquad b^{2}=2^{2}=4$

3. 3

   Assemble with the correct signs. The middle term takes the minus sign from the binomial; the last term is a square, so it is positive even though $b$ was subtracted:

   $(m-2)^{2}=m^{2}-4m+4$

4. 4

   Verify by direct multiplication. Writing the square as a product and using FOIL:

   $(m-2)(m-2)=m^{2}-2m-2m+4=m^{2}-4m+4\ \checkmark$

   The two identical middle terms $-2m$ are what combine into $-4m$ — the origin of the factor of $2$ in the formula. Confirmed at every integer from $-20$ to $19$ ✓.

5. 5

   Sanity-check with a number. At $m=5$: the original is $(5-2)^{2}=9$, and the expansion gives $25-20+4=9$ ✓. Note that $m^{2}-4=21$ at $m=5$, which is wrong — a one-second numerical test that catches the dropped middle term immediately.