Question

Is the following problem simplified correctly? (5x+7)(5x-7)=25x2+70x-49

Answer 1

no.
(a+b)(a-b) = a^2 - b^2. there is no ab term.

Answer 2

@bdboy, same as before... when you have the product of a sum and difference of binomials you have a factored form of a difference of two squares, that is, the product is a difference of two squares (se the right side of dhatraditya's formula?)

Answer 3

in your problem a=5x and b=7

Answer 4

yes,
(a+b)(a-b) = a^2 +ba -ab - b^2 = a^2 +ab-ab-b^2 = a^2-b^2

Answer 5

when you have the product of a sum and difference of binomials, the middle two terms of the FOIL will always cancel each other out

Answer 6

thanks a ton i really appreciate you not just giving me the answers but actually explaing how to get them which helps me understand it so much more...

Answer 7

you need to multiply 25 and 2 then subtract 49

Answer 8

ok, what's the product

Answer 9

do you want me to show you

Answer 10

it think i totally just screwed it up.. somehow i got 1 but thats not correct

Answer 11

please that would be most helpful

Answer 12

that is the correct answer for zac's question

Answer 13

once you realize you have a difference of squares you just write\[(5x-7)(5x+7)=(5x)^2-7^2=25x^2-49\]with practice you would most likely do the middle step as a mental calculation

Answer 14

notice on the foil how the middle two terms cancel out\[(5x-7)(5x+7)=25x^2+35x-35x+49=25x^2-49\]

Answer 15

if I may, with mandolino's permission,

\[(a+b)(a-b) = a(a-b) + b(a-b) = a^2 -ab + ba -b^2\]
\[= a^2 - ab + ab -b^2 = a^2 - b^2\]

Answer 16

note that i just noticed a sign error in my previous post: the +49 in the middle step should be -49; the final answer is correct

Answer 17

@dhatraditya, i've just been playing off your posts

Answer 18

:)

Answer 19

bdboy try this one: (2x-3)(2x+3)

Answer 20

i'm going to give the answer in my next post, so don't look if you are trying it on your own!

Answer 21

\[(a-b)(a+b)=a^2-b^2\]in my example a=2x and b=3\[(2x-3)(2x+3)=(2x)^2-3^2=4x^2-9\]

Answer 22

can you try one more except let me put the answer down