Math help

'Defy · Jun 15, 2011

I need to develop these two question:
l) (2x + 3)(x - 9)
ll) -4(x +2)Â²

I also need to factorize these two:
l) -xÂ² -2x + 35
ll) 3xÂ² - 75

I don't understand either one, so if you could also explain how you get the answer, that would be great so I can use this as an example in the future

Many thanks!

Austintheman · Jun 15, 2011

Is this algebra? If it is i can see if i can help :O

anqel · Jun 15, 2011

example of develop.

This is algebra, so idk how you learn to do it but i would use FOIL

F- first ( multiply the first numbers in each)
O- outer (mulitply the numbers farthest away from eachother)
I- inner (multiply the numbers closest to eachother)
L- Last (multiply the last number in each bracket)

So (2x + 3) (x - 9)

F ..... 2x * x = 2x^2
O ..... 2x * -9 = -18x
I ...... 3 * x = 3x
L ..... 3 * 9 = 27

lay out into one equation (put + for the postive ones and - for the negative ones)

like so:

2x^2 - 18x + 3x + 27

(put together common variables)

2x^2 (-18x + 3x) + 27

2x^2 -15x + 27

And thats your answer.

ET Phone Home · Jun 16, 2011

Sometimes things are best without accompanying text. Use the following solution progression as a supplement to the above explanation.

l) (2x + 3)(x - 9)
= 2x2 -18x +3x -27
= 2x2 - 15x - 27

ll) -4(x +2)Â²
= -4(x+2)(x+2)
= -4(x2+2x+2x+4)
= -4(x2+4x+4)
= -4x2 - 16x - 16

lol@ "factorize," feel free to just say "I need to factor these"

l) -xÂ² -2x + 35
In general its not good to have a negative leading coefficient. Factor out a negative sign:
-(x2 +2x -35)
You need a pair of numbers which multiply to negative 35 and add to 2.
1, -35
-1, 35
5, -7
-5, 7
7 and -5 work:
-(x+7)(x-5)

Solutions are -7 and 5 (where either binomial is equal to zero)

ll) 3xÂ² - 75
As was the case in the precious problem, where the leading coefficient was -1, we had problems. Just like in the last problem, let's factor out something from the expression so that the x^2 term has a coefficient of 1:

3(x2 - 25)

Here you have an expression of the form (x2 - a2), where a is some number (in this case 5, since 5^2 =25). This is one of those handy dandy circumstances that you need to memorize:

(x2 - a2) = (x + a)(x - a)

So your factored expression is:

3(x-5)(x+5)

Solutions are 5 or -5