Answer: a
Step-by-step explanation:
[tex]\text{First, let's see what}\ (a-2b)^2\ \text{expands to:}\\(a-2b)(a-2b)=a^2-4ab+4b^2\\\\\text{If you add 8ab (option a), you get:}\ a^2+4ab+4b^2\\\\\\\text{Now, let's look at the equations on the right side:}\\(a+2b)^2=a^2+4ab+4b^2\\\bold{\text{We see that option (a) is TRUE}}\\\\\\\text{We can see that options b and d do not match. Let's check option c:}\\(a+2b)^2=a^2+4ab+4b^2\\\text{This is not a match.}[/tex]
[tex]a)\ (a-2b)^2+8ab=(a+2b)^2\\a^2+4ab+4b^2=a^2+4ab+4b^2\ \checkmark\\\\b)\ (a-2b)^2=a^2-4b^2\\a^2+4ab+4b^2\neq a^2-4b^2\\\\c)\ (a-2b)^2=(a+2b)^2\\a^2-4ab+4b^2\neq a^2+4ab+4b^2\\\\d)\ (a-2b)^2\=a^2+4b^2\\a^2-4ab+4b^2\neq a^2+4b^2[/tex]
