Math question please?

Question

How would you "expand" the following questions? Plese explain to me. I will ask for help on monday! but i need to finish the sheet.

1. (x+5)^2
2. (x+1)^2
3. (3x+2)(3x-2)


Square each binomial:

1. x+7
2. 2x-1

Expand:

(c+1/2)(c-1/2)

Expand:

3(x-2)^2

-3(5-n)^2

Answer 1

(c+1/2)(c-1/2)

ANS: c^2 - (1/4)


3(x-2)^2

ANS: 3x^2 - 12x + 12



-3(5-n)^2

ANS: +3n^2 + 30n - 70


(x+5)^2

ANS: x^2 + 10x +25


(x+1)^2

ANS:x^2 +2x+1


(3x+2)(3x-2)

ANS: 9x^2-4

NOTE: You should learn and study it

Answer 2

1. (x+5)² = (x + 5) (x+ 5) =
x² + 10x + 25 = 0
delta = 10² - 4.1.25
delta = 100 -100
delta = 0

x =( -10 +/- 0) : 2
x' = x" = -10 : 2 = -5
Solution: There are two Real and equal roots: x' and x" = -5.
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2. (x+1)² = (x + 1)(x+1) =
x² + 2x + 1 = 0
delta = 2² - 4.1.1
delta = 4 - 4 =0

x = (-2 +/- 0) : 2
x' = x" = -2: 2 = -1
Solution: There are two Real and equal roots: x' and x" =-1.
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3. (3x+2)(3x-2)
(3x)² - (2)² = 9x² - 4
x² = 4/9
x = 2/3 or -2/3
Solution: {x elements of R | x = 2/3 or -2/3}
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1. x+7 = (x+7)(x+7) = (x+7)²
2. 2x-1 = (2x-1)(2x-1) = (2x-1)²
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(c+1/2)(c-1/2)
c² - (1/2)² =
c² -1/4 = 0
c² = 1/4
c = 1/2 or -1/2
Solution: {There is "c" in R | c = 1/2 or c = -1/2}
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3(x-2)² =
3(x² - 4x + 4) =
3x² - 12x + 12 = 0
delta = 144 - 4.3.12
delta = 144 - 144
delta = 0

x = (12 +/- 0) : 2.3 = 6
Solution: There are two Real and equal roots: x' and x" = 6.
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-3(5-n)² =
-3(25 - 10n + n²) =
-75 + 30n -n² = 0
n² -30n + 75 = 0
delta = 30² - 4.1.75
delta = 900 - 300
delta = 600
n = (30 +/- 10\/6) : 2
n' = (30 + 10\/6) : 2 = 15 + 5\/6
n" = (30 - 10\/6) : 2 = 15 - 5\/6
Solution: {n elements of R | n = 15 + 5\/6 or n = 15 - 5\/6}
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Answer 3

1. (x+5)^2
(x+5)^2 = (x+5)(x+5) = x^2 +10x+25
means there Do FOIL (First, Outer, Inner, Last)
are two (multiply the First two numbers,
Then Outer, Then Inner, Then last and
add them all together)
2. (x+1)^2 -- Same as above
3. (3x+2)(3x-2) -- just do FOIL


Square each binomial:

1. x+7 = (x+7)(x+7) = Do FOIL
2. 2x-1 = (2x-1)(2x-1) = Do FOIL

Expand:

(c+1/2)(c-1/2) = (FOIL) c^2 - 1/4


Expand:

3(x-2)^2 = FOIL then multiply by 3 because of PEMDAS, you will do the exponestials before you do the multiplication of the 3
First FOIL : 3[x^2 - 4x +4]
Multiply : 3x^2 - 12x + 12

-3(5-n)^2
Same as above except (5-n) is really (-n+5)

Answer 4

1. (x+5)^2 = (x+5)(x+5)
*Use the foiling method...

(x)(x) + (x)(5) + (5)(x) + (5)(5)
x^2 + 5x + 5x + 25
x^2 + 10x + 25

2. (x+1)^2 = (x+1)(x+1)

(x)(x) + (x)(1) + (1)(x) + (1)(1)
x^2 + x + x + 1
x^2 + 2x + 1

3. (3x+2)(3x-2) > give it a try-its the same format as (#1- #2)

Square each binomial:

4. (x+7)^2 = (x+7)(x+7)

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

5. (2x-1)^2 > give it a try

Expand:

6. (c+1/2)(c-1/2)

(c)(c) + (c)(-1/2) + (1/2)(c) + (1/2)(-1/2)
c^2 - c/2 + c/2 - 1/4
c^2 - 1/4

7. 3(x-2)^2 = 3(x-2)(x-2)

3[(x)(x) + (x)(-2) + (-2)(x) + (-2)(-2)]
3(x^2 - 2x - 2x + 4)
3(x^2 - 4x + 4)

3(x^2) - 3(4x) + 3(4)
3x^2 - 12x + 12

8. - 3(5-n)^2 - give it a try

Answer 5

Use the technique called FOIL
I will work the first problem you can do the rest.

(x + 5)(x + 5)

first x * x = x^2
outside x * 5 = 5x
inside 5 * x = 5x
last 5 * 5 = 25

you get x^2 + 5x + 5x + 25

combine like terms 5x + 5x = 10x therefore

x^2 + 10x + 25

every problem is done the same way but the last 2 problems require 1 more step ignore the outside number until you have foiled the expressions in the parenthesis then multiply through by that number. good luck

Answer 6

1) (x+5)*(x+5) = x^2 +5x+5x+25=x^2+10x+25
2) (x+1)(x+1) = x^2+x+x+1=x^2+2x+1
3) (3x+2)(3x-2)=9x^2-6x+6x-4=9x^2-4
4) (x+7)^2= (x+7)(x+7)=x^2+14x+49

Basically to sqauer any binomial
(x+y)^2 = x^2 + Y^2 + 2xy AND
(x-y)^2 = x^2 + y^2 - 2xy

Hope this helps. Are you trying to do your homework on yahoo ? :)

Answer 7

First, do you remember FOIL? with #1, you need to rewrite the square of (x+5) as the product of two binomials, so (x+5) (x+5)= then use FOIL to simplify it. do the same for #2. #3 is ready to FOIL: So multiply the first terms, 3x * 3x= 9x^2, then multiply the outer terms, 3x * (-2) = -6x, then multiply the inner terms, 2 * 3x=6x, then multiply the last terms, 2* -2, combining like terms, you get 9x^2 -4

Answer 8

(x+5)^2= x^2 + 25 + 10x
(x+1)^2= x^2 + 1 + 2x
(3x+2)(3x-2)= 9x^2 - 4
x+7 square = x^2 + 49 + 14x
2x-1 Square = 4x^2 + 1 - 4x
(c+1/2)(c-1/2)= c^2 - 1/4
3(x-2)^2= 3(x^2 + 4 - 4x) = 3x^2 + 12 - 12x
-3(5-n)^2 = -3 (25+ n^2 - 10n) = -75 - 3n^2 + 30n

Answer 9

1. (x+5)(x+5)
= x^2 + 10x + 25

2. (x+1)(x+1)
= x^2 + x + 1