Question

Resolve into factors
( a +2b )²- ( 2a - b )²​

Answer 1

Answer: Hey mate the answer is $-3a^2+3b^2+8ab$

Step-by-step explanation:

$(a+2b)^2 - (2a-b)^2$

by the identities of (a+b)^2 and (a-b)^2

$=a^2+4b^2 +4ab - (4a^2+b^2-4ab)\\=a^2+4b^2+4ab-4a^2-b^2+4ab\\=-3a^2+3b^2+8ab$

Now explanation time,

So in the first step I have used the identities of (a+b)^2 and (a-b)^2 and opened them as you can see above

then in the second step I have opened the bracket of (2a-b)^2 and changed its signs as there is minus sign before the brackets as u can see clearly

now in the third step I have simplified all of the terms and got the answer,

$-3a^2+3b^2+8ab$

So the above one is the answer of your question.

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