Question

vgh

Answer 1

@sarahusher

Answer 2

Sorry, @sarahusher you proceed..

Answer 3

Use FOIL to find your answer and compare them both

Answer 4

I need to compare & contrast this question in complete sentences I got it wrong because I didn't put enough specific details for the differences & similarities..

Answer 5

See, in first expression you have x^2 terms but no x term, but in second you got x^2, x as well as constant term..

Answer 6

In doing (a-b)(a+b), always Middle two terms get cancelled, while in (a+b)(a+b), middle term adds up..

Answer 7

So they are both of similar shapes, (ie the typical X^2 'U' shape) however one of the main things to notice is that
x^2 -16 has two distinct roots and goes into negative quadrants
whereas the other one has one distinct root (albeit a same root as the other) but remains completely in the positive quadrants

Try plotting them, it'll be pretty obvious what the differences and similarities are :)

Answer 8

@sarahusher my teacher said it was fine except I didn't put any specific details in the differences section! I know the similarities & she said they were fine I just need help getting the differences!

Answer 9

here is some differences:
(a+b)(a+b) = positive constant
(a-b)(a+b) = negative constant
(a-b)(a-b) = positive constant
notice how we get a positive constant when we either multiply our b by (+)(+) or
(-)(-)

Answer 10

Firstly,
x^2 + 8x + 16 appears only in positive quadrants
x^2 -16 appears in both positive and negative quadrants

x^2 + 8x + 16 has one root
x^2 -16 has two roots

they are some differences :)
do you mean differences like this?

Answer 11

@sarahusher what do you mean x^2 + 8x + 16 has one root??? & the other answer has two roots what exactly does that mean? :/

Answer 12

Well if you draw them you can clearly see that
(x^2 -16) cross the axis at x=4 and x=-4 which tell us that it has two distinct roots
(x^2 +8x+16) has a repeated root, ie only crosses the axis once at x=-4

this isn't geometrically so significant, but it's certainly a difference worth noting

Answer 13

by using difference of two squares:
(a+b)(a-b)= a^2 - b^2
so your q is:
(x+4)(x-4)
= x^2 - 4^2
= x^2 - 16