Question

PSAT Question:
Why does -2(x+3)^2 equal 4(x+3)^2?

Answer 1

Does -2(x + 3)^2 = 4(x + 3)^2 ?

Answer 2

They appear to be offset from each other by six units:

-2(x + 3)^2 + 6(x - 3)^2 = 4(x + 3)^2

Answer 3

Try your best to make sense of it

Answer 4

So -2(x+3)^2 does equal 4(x+3)^2 ?

Answer 5

No. That will never happen.

Answer 6

@Yttrium then why does the problem's explanation say that?

Answer 7

Think of the question as follows:
Given y = (x+3)^2
Find (-2x-6)^2
(-2x-6)^2 = { -2(x+3) }^2 = (-2)^2 * (x+3)^2 = 4 * y
(because it is given that y = (x+3)^2)

Answer 8

It doesn't. It says that

\[[-2(x + 3)] ^2= 4(x + 3)^2\] which is slightly different from what you posted.

Answer 9

Understand that \([-2(x + 3)] ^2\) is different from \(2(x + 3)^2\)

Answer 10

@pabloecortez07 always take note that parentheses are really important in mathematical expressions. Because absence of it may lead to misinterpretation.. Just like what happened. It may also lead to wrong answer.

Answer 11

Similarly there's a difference between \((ab)^2\) and \(ab^2\)

Recall the following rule of exponents:
\((ab)^2 = a^2b^2\)

Answer 12

Ah ok, now I understand. Thank you very much! I'll keep in mind to always be careful when dealing with parentheses.

Answer 13

Exactly which explanation did you understand?

Answer 14

I liked the one where you say that
(ab)^2 = a^2b^2 since I understand that

[-2(x+3)]^2 = 4(x+3)^2

Since -2^2 is 4

And (x+3)^2 is equal to (x+3)^2

Answer 15

Okay, very good.

Answer 16

Thank you.