1. ## Quadratic formula 4(a+b)±√(16(a²+2ab+b²)-48ab) / 24

Hi,

I have a question in regard to a quadratic formula I'm solving.

4(a+b)±√(16(a²+2ab+b²)-48ab) / 24

4(a+b)±4√(a²-ab+b²) / 24

I don't understand how +2ab became -ab and why -48ab disappeared.

Anyone able to clarify that for me?

Thanks
David

2. Hello Splint

Welcome to Math Help Forum!
Originally Posted by Splint
Hi,

I have a question in regard to a quadratic formula I'm solving.

4(a+b)±√(16(a²+2ab+b²)-48ab) / 24

4(a+b)±4√(a²-ab+b²) / 24

I don't understand how +2ab became -ab and why -48ab disappeared.

Anyone able to clarify that for me?

Thanks
David
Just remove the inner brackets inside the square root and simplify:

$\sqrt{\Big(16(a^2+2ab+b^2)-48ab\Big)}$

$=\sqrt{(16a^2+32ab+16b^2-48ab)}$

$=\sqrt{16a^2 -16ab+16b^2}$

$=\sqrt{16}\sqrt{a^2-ab+b^2}$

$=4\sqrt{a^2-ab+b^2}$