Math Help - Quick Polynomial simplifying question

1. Quick Polynomial simplifying question

Hey guys,
Just a quick one.. brain freeze on what to do in this case..

=3-2(8x^2-1)^2
Now, will I apply the exponent first, or the 2? And if apply the exponent first, what will I multiply the 2 by.. the entire product of the exponent?

I seem to remember from my math laws that you have to expand the brackets first, but I am unsure if this includes the 2 outside the bracket..

Thanks

2. expand, then multiply each term of the entire product by 2

3. Thanks..

wow, and really basic, but my brain just isn't working..

3-2(64x^4-16x^2+1) (You would multiply everything in the brackets by positive 2, Correct?)

=3-128x^4 -32x^2 -2
= -128x^4-32x^2+1 (Correct?

4. Originally Posted by Slipery
=3-2(8x^2-1)^2
What came before the "equals" sign? What were the instructions?

I think you were supposed to "simplify" or "expand" the polynomial expression. If so, the order of operations says that you have to apply exponents first, so the squaring on the parentheses (to multiply out the polynomial squaring) comes before doing the multiplication in front of the parentheses.

. . . . . $(8x^2\, -\, 1)^2$

. . . . . $(8x^2\, -\, 1)(8x^2\, -\, 1)$

. . . . . $(8x^2)(8x^2)\, +\, (-1)(8x^2)\, +\, (8x^2)(-1)\, +\, (-1)(-1)$

. . . . . $64x^4\, -\, 16x^2\, +\, 1$

Then you deal with the multiplication out front:

. . . . . $-2(64x^4\, -\, 16x^2\, +\, 1)$

. . . . . $-128x^4\, +\, 32x^2\, -\, 2$

. . . . . $3\, -\, 128x^4\, +\, 32x^2\, -\, 2$
. . . . . $-128x^4\, +\, 32x^2\, +\, 1$