Question

Could someone please help me simplify 3-2(3x-4)(3x+4)-(x+2)(2x-1)?

Answer 1

Do you know the foil rule for expanding brackets?

Answer 2

yes so I got 3-2(9x^2+12x-12x+16)-(2x^2-x+4x-2) is that correct?

Answer 3

Yep thats right, now just times the number outside the brackets by everything inside.

Answer 4

Simplify the inside of the brackets firstb to make it easier

Answer 5

do you minus 3-2 first? .....so it would be 1(9x^2+12x-12x+16)-(2x^2-x+4x-2)?

Answer 6

oh

Answer 7

(9x^2+16)-(2x^2+3x-2)

Answer 8

No you can't do that, the -2 is multiplies by brackets its a different type of term than the 3 by itslef, so you cant add them

Answer 9

yeah what you did was right

Answer 10

ok now do I multiply the first bracket with -2?

Answer 11

but remeber only add things if they have the same thing, for example x^3 and x^2 cant add together, but x^2 and 2x^2 can add to 3x^3

Answer 12

onceyou multiply the bracket by -2 you can start combining like terms (same power of x)

Answer 13

but what about the 3?

Answer 14

on the outside?

Answer 15

leave that to last, you can only combine it with other numbers by itself (not multiplied by an x)

Answer 16

so right now I am getting 3(-18x^2+32)-(2x^2-x+4x-2)

Answer 17

just leave the 3, and you forgot about the x in the first bracket

Answer 18

but it cancels out doesn't it? because 12x-12x is 0

Answer 19

oh yeah true that i forgot :P

Answer 20

haha its ok

Answer 21

So you have 3-2(9x^2+12x-12x+16)-(2x^2-x+4x-2)
this becomes 3 -2(9x^2 + 16) -(2x^2+3x-2)
this becomes 3 -(18x^2-32) -2x^2-3x+2
this becomes 3 -18x^2 + 32 -2x^2 -3x +2

Answer 22

Now combine like terms

Answer 23

i make a mistake

Answer 24

it should be -32

Answer 25

on the last line (i screwed up a couple of lines up)

Answer 26

no its positive

Answer 27

its +32

Answer 28

-2 x 16 = -32

Answer 29

-2x-16=32

Answer 30

of i see what was wrong

Answer 31

because at the beginning its (3x-4)(3x+4)

Answer 32

i accidentaly put +16 when it was -16

Answer 33

and when you multiply them together its -16

Answer 34

yeah

Answer 35

multiplied with -2 is 32

Answer 36

sorry for the mistake :P

Answer 37

am i correct? haha

Answer 38

its ok!!! :)

Answer 39

yeah ur right

Answer 40

so would the answer be -20x^2+3x+33

Answer 41

Yep but should the x one be -3x?

Answer 42

yeah its -3x

Answer 43

how?

Answer 44

other than that your right, good job

Answer 45

in last brackets 4x - x = 3x
as theres a negative in front it becomes -3x

Answer 46

in front of the brackets

Answer 47

im confused

Answer 48

I got -x+4x

Answer 49

which gives you 3

Answer 50

You have -(x+2)(2x-1)
this becomes -(2x^2-x+4x-2)
multiplying everyhting by -1
it becomes -2x^2 +x -4x +2
=-2x^2-3x+2

Answer 51

why did you multiply everything by -1

Answer 52

when you have brackets and a number outside like a(b+x) , to expand you multiply b and x by a. Outside those brackets theres a -, this just means -1*(2x^2-x+4x-2), therefore everything is multiplied by -1.

Answer 53

ohhhh ok i get it now

Answer 54

Ok cool

Answer 55

so the answer would now be -20x^2-3x+37

Answer 56

yep :)

Answer 57

since you are helping me do you mind helping me with one more math question? please and thank you

Answer 58

Ok if you want

Answer 59

so now its factoring polynomial expressions and it asks to factor by finding the greatest common factor. and the expression is 12x^2y^2-18x^3y+24x^2y

Answer 60

Thank you for your help

Answer 61

I appreciate it

Answer 62

Ok now factoring is just the reverse of the expanding thing I showed you. Expanding is when you have a number multiplied against brackets and then bringing it all out into a polynomial. Factoring is when you have a plynomial and you turn it into a brackets multiplied against a number.

Answer 63

You're very welcome btw, im glad to help

Answer 64

so could you help me go through this question step by step so that i will get a hang of it please

Answer 65

Ok

Answer 66

First you have to find one number that exist in all 3 terms.

Answer 67

all the terms have x^2 right?

Answer 68

the middle one is just X^2 x X

Answer 69

to get X^3

Answer 70

however the highest y power is only 1 two have y^1 and one has y^2

Answer 71

this middle one is different

Answer 72

all the terms have a multiple of 6, 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24

Answer 73

yes

Answer 74

Ok those are the common factors, you have to find the highest multiple of every variable (in this case x and y) and the highest multiple of the coefficents

Answer 75

This means that we can multiply (x^2)(y)(6) by different things to get all the terms

Answer 76

Does that make sense?

Answer 77

just a little bit

Answer 78

Ok you will get it better in the next step.

Answer 79

where did you get 6 from?

Answer 80

Now that we have the highest common factor, we have to find what these multiply against to get each term.

Answer 81

oh 6 is the common factor

Answer 82

The 6 is the highest factor of the coeffeicents of each term, it multiplies to make 12 18 and 24

Answer 83

yes

Answer 84

Ok (x^2)(y)(6) * (a+b+c) = the original expression you gave me

Answer 85

what does (x^2)(y)6 times against to make 12x^2y^2 ?

Answer 86

?

Answer 87

wait what

Answer 88

12?

Answer 89

6(x^2)(y) is the common factor (highest), this means that it can times against a number to make each of the terms

Answer 90

6 x 2 makes 12

Answer 91

so the coeffcient must be 2

Answer 92

x^2 x 1 = x^2 , we dont worry about this one

Answer 93

y x (y ) = y^2

Answer 94

are you looking at 12x^2y^2 only?

Answer 95

I am confused to which section of the expression you are explaining to me

Answer 96

So the number that 6y(x^2) multiplies agasint to make 12x^2y^2 is 2y

Answer 97

we are taking each term 1 by 1

Answer 98

This seems a bit tedious, ill make an easier example so you understand whats going on ok?