FRUSTRATED ALGEBRA STUDENT help please?

Question

17.)(2m+2)(2m-2)

20.)(a+8^2)

23.)(3b-1)(3b+1)

29.)(3t+1)^2

41.)(3+2x)(3-2x)

42.)(2s-4)^2

63.)(4b-3)^2

68.)(x-7)^2

Answer 1

The easiest approach is to remember FOIL, which stands for First, Inner, Outer, Last

(a+b)(c+d) = ac + bc + ad + bd

ac are the first elements of each group
bc are the "inner" elements
ad are the "outer" elements and
bd are the last elements of each group

Take a quick look at number 20, (a + 8^2). The only simplification we can perform is to square the 8 and get (a + 64). Technically there is no algebra involved in this, other than the fact that our answer retains a variable.

For the questions in the for (a + b)^2, you can rewrite them as (a + b)(a + b) and perform the FOIL method.

Let's work through number 17: (2m + 2)(2m - 2)

Multiplying the First elements we get 2m*2m = 4m^2
Multiplying the Inner elements we get that 2*2m = 4m
Multiplying the Outer elements we get that 2m*(-2) = -4m
Multiplying the Last elements, we get that 2*(-2) = -4

So our answer would be: 4m^2 + 4m + (-4m) + (-4)
which we can simply to just 4m^2 - 4

Some teachers may want you to pull out the common factor of 4 and write this as 4(m^2 - 1).

See if you can apply FOIL to some of the other one's on your own. I'm providing answers to them all below so you can check your work to make sure it's right, but try them first so you can get comfortable with the idea.



Answers:
17) 4m^2 - 4
20) (a + 64)
23) (9b^2 - 1)
29) 9t^2 + 6t + 1
41) -4x^2 + 9
42) 4s^2 -16s + 16
63) 16b^2 - 24b + 9
68) x^2 - 14x + 49

--charlie

Answer 2

Hi,

17.)(2m+2)(2m-2)
4m^2 - 4m + 4m - 4
4m^2 - 4

When binomials are the same except for one + and one - in the middle, you don't have to "FOIL". All you have to multiply are the firsts and the lasts because the 2 in the middle drop out!!

20.)(a+8^2)
I assume this was supposed to be (a + 8)^2. On this one, you have to foil it all out.
(a + 8)(a + 8) = a^2 + 8a + 8a + 64 = a^2 + 16a + 64


23.)(3b-1)(3b+1) Do the shortcut, like on #17.
Just do first x first and last x last

3b * 3b - 1*1 =
9b^2 - 1

29.)(3t+1)^2 Do it out the long FOIL way:

(3t + 1(3t + 1) = 9t^2 + 3t + 3t + 1 = 9t^2 + 6t + 1

41.)(3+2x)(3-2x) Shortcut: firstfirst - lastlast
9 - 4x^2

42.)(2s-4)^2 the long FOIL way!!

(2s - 4)(2s - 4) = 4s^2 - 8s - 8s + 16 = 4s^2 - 16s + 16

63.)(4b-3)^2 Long way!!

(4b - 3)(4b - 3) = 16b^2 - 12b -12b + 9 = 16b^2 - 24b + 9

68.)(x-7)^2 Long way!!

(x - 7)(x - 7) = x^2 - 14x + 49



I hope that helps you!!! Keep practicing!! :-)

Answer 3

"For the lover of challenge, last year's courseload will always be easy, this year's courseload will always be tedious and next year's will be downright hard or impossible."
- adapted some math blog.
You should really try harder than that - it takes longer to type than to multipy out manually. Anyway, if you want answers, here they are. I'm sympathetic because many would be uneasy about 68 math problems at their own level.

17
4mm - 4
20
aa + 16a + 64
23
9bb - 1
29
9tt + 6t + 1
41
9 - 4xx
42
4ss - 16s + 16
63
16b - 24b + 9
68
xx - 14x + 49

Answer 4

17. m = -1 and m = 1
20. a = -64
23. b = 1/3 and -1/3

just make everything = 0

Answer 5

4m^2 - 4
9b^2 -1
9t^2 + 6t +1
9 - 4x^2
4s^2 - 16s + 16
16b^2 - 24b + 9
x^2 - 14x + 49

Answer 6

4m^2 - 4

a + 16

9b^2 - 1

9t^2 + 6t +1

9 - 4x^2

4s^2 - 16s - 16

16b^2 - 24b + 9

x^2 - 14x + 49

Answer 7

You should look over this website!! It was made by a teacher for students to overcome any issues with math!! I found it last night.

Answer 8

I recommend asking your instructor if he/she would concepts spending approximately 10 minutes after type to describe issues to you and according to danger refer some prepare routines. don't be shy to ask! that's what instructors are there for.

Answer 9

Classes and problems are difficult when you neither read the book or pay attention to your teacher.

Answer 10

multiply them out buddy. you should be able to do these. remember foil. first outter inner last. and watch the negitive signs.