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Choose the correct product of (5x + 4)2. 25x2 + 40x + 16 25x2 − 16 25x2 + 16 25x2 − 40x + 16

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(5x+4)(5x+4) Do you know how to use the FOIL method?
First, Outer, Inner, Last. Your first terms that you need to multiply are 5x and 5x 5x*5x = 25x^2 Your outer terms that you need to multiply are 5x and 4. 5x*4 = 20x Your inner terms that you need to multiply are 5x and 4. 5x*4 = 20x You last terms that you need to multiply are 4 and 4. 4*4 = 16 So you have 25x^2, 20x, 20x, and 16 that you need to "combine." 25x^2 +20x +20x +16 = 25x^2 +40x +16

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Other answers:

ah wow thanks so much!
Watch this :-)
is this correct
i still dont nderstand @phi
  • phi
i dont know anything?
  • phi
see Khan's vide if you have time
i know that \(\color{lime}{\huge\ (5x+4)^2~}\) = 25x^2+16 but i dont understand if i add a 40x
in FOIL i use 5x^2+4^2 but dont get why did they add a 40x?
  • phi
do you know what you get when you multiply a(x+y)
  • phi
yes. now what if a was "complicated" in other words, if a was short-hand for (c+d) ? we would get (c+d)x + (c+d)y (I just replaced "a" with its equivalent (c+d) ) now we do the "distributive property" again: (c+d)x is the same as x(c+d), or, xc +xd and (c+d)y is cy + dy
  • phi
in other words (c+d)(x+y) can be written as xc + xd +yc +yd we get FOUR terms (which would come from using FOIL, if you learn that)
foil is first out inner last
  • phi
with (5x+4)(5x+4) we will get 4 terms, but we can combine two of the terms, and get 3 terms in the end
BTW i hope you dont ge confused cuz it looks like (5x + 4)•2 but it is (5x + 4)^2
  • phi
let's use the distributive idea to do (5x+4)(5x+4) First, let a= (5x+4) so it's easier to see what we are doing: a(5x+4)= a*5x +a*4 now replace a with (5x+4) (5x+4)*5x + (5x+4)*4 now expand both terms: can you do that ?
5x(5x+4)+4(5x+4) 25x^2•20x+20x+16 ohhhhhh thx @phi
  • phi
the first part 5x(5x+4) is written as 25x^2 +20x so you get all together \[ 25x^2 +20x +20x +16\] the last step is notice we have 20 x's plus 20 more x's which is 40 x's. we write \[ 25x^2 +40x +16\]

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