Find the LCM of $$ a^{2}-4 b^{2} $$ and $$ a^{2}+4 a b+4 b^{2} $$ OA. $$ (a+2 b) $$ OB. $$ (a-2 b)(a+2 b)^{2} $$ OC. $$ (a+2 b)^{2} $$ OD. $$ (a-2 b)(a+2 b) $$

Question

UpStudy AI · Accepted Answer

We start by factoring each expression.

1. Factorize $$ a^2 - 4b^2 $$:
   $$
   a^2 - 4b^2 = (a - 2b)(a + 2b)
   $$

2. Factorize $$ a^2 + 4ab + 4b^2 $$:
   $$
   a^2 + 4ab + 4b^2 = (a + 2b)^2
   $$

To find the least common multiple (LCM), we take each factor raised to the highest power it occurs in either expression:

- The factor $$(a - 2b)$$ appears once in $$a^2 - 4b^2$$ and not at all in $$a^2 + 4ab + 4b^2$$. Thus, include $$(a - 2b)^1$$.
- The factor $$(a + 2b)$$ appears once in $$a^2 - 4b^2$$ and twice in $$a^2 + 4ab + 4b^2$$. Thus, include $$(a + 2b)^2$$.

Hence, the LCM is:
$$
(a - 2b)(a + 2b)^2
$$

The correct answer is option OB: $$(a - 2b)(a + 2b)^2$$.
The LCM is $$(a - 2b)(a + 2b)^2$$.

Find the LCM of and
OA.
OB.
OC.
OD.

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions

Find the LCM of and OA. OB. OC. OD.