Algebra 1 Jeopardy

Multiplying binomials

100

(x + 3)(x + 8)

x² + 11x + 24

(x+3)(x−8) becomes:

(x×x)−(x×8)+(3×x)−(3×8)

x2−8x+3x−24

We can now combine like terms:

x2+(−8+3)x−24

x2−5x−24

200

(x - 12)(x - 7)

x² - 19x + 84

300

(x - 12)(x - 7)

x² - 19x + 84

(x−12)(x−7)

Apply the distributive property by multiplying each term of x−12by each term of x−7.

x2−7x−12x+84

Combine −7x and −12x to get −19x.

x2−19x+84

400

(x + 4)(x + 8)

x² + 12x + 32

500

(3x – 1)(x + 5)

3x2 + 14x - 5

Multiplying polynomials

100

(2y - 7)(3y + 5)

-8x³y + 6x²y² - 2xy³

200

(2x + 3)(x + 5)

2x2 + 13x + 5

300

(3r-4)(7r-5)

21r2-43r+20

(3r−4)(7r−5)

Apply the distributive property by multiplying each term of 3r−4by each term of 7r−5.

21r2−15r−28r+20

Combine −15r and −28r to get −43r.

21r2−43r+20

400

x3(2x2+3x)=

2x5+3x4

500

(x + 7)2

x2 + 14x + 49

(x+7)2

This can be rewritten as:

(x+7)(x+7)

Multiply the first terms in each expression.

(x+7)(x+7)

x⋅x=x2

Now we move to outside . multiply the outside terms of each expression.

(x2+7)(x2+7)

x2⋅7=7x2

Next up are the inside terms. Multiply these from each expression.

(x2+(7))(x2+7)

7⋅x2=7x2

Finally, we have the last terms. Multiply the last terms from each expression.

(x2+7)(x2+7)

7⋅7=49

Now combine all of the solutions that we have come up with.

x2+7x2+7x2+49

Combine the like terms in between.

x2+14x+49

Solving Systems by Elimination

100

y=5x+3    y=-2x-4

-1

200

7x+y=-9    -3x-y=5

Answer : {-2,-1}

Solve equation [2] for the variable  y  
 

  [2]    y = -2x - 4

Plug this in for variable  y  in equation [1]

   [1]    (-2x-4) - 5x = 3
   [1]     - 7x = 7

 Solve equation [1] for the variable  x  

   [1]    7x = - 7

   [1]    x = - 1

 By now we know this much : 

    y = -2x-4
    x = -1

 Use the  x  value to solve for  y  

    y = -2(-1)-4 = -2

Solution :

 {y,x} = {-2,-1} 

300

4x+4y=4    3x+4y=10

Answer:{-6,7}

Solve equation [2] for the variable  y  
 

  [2]    4y = -3x + 10

  [2]    y = -3x/4 + 5/2

Plug this in for variable  y  in equation [1]

   [1]    4x + 4•(-3x/4+5/2) = 4
   [1]    x = -6

Solve equation [1] for the variable  x  

   [1]    x = - 6

By now we know this much : 

    x = -6
    y = -3x/4+5/2

Use the  x  value to solve for  y  

    y = -(3/4)(-6)+5/2 = 7

Solution :

 {x,y} = {-6,7} 

400

-9x-4y=-20     5x+4y=4

Answer:(4,-4)

Solve equation [2] for the variable  y  
 

  [2]    4y = -5x + 4

  [2]    y = -5x/4 + 1

 Plug this in for variable  y  in equation [1]

   [1]    -9x - 4•(-5x/4+1) = -20
   [1]    -4x = -16

Solve equation [1] for the variable  x  

   [1]    4x = 16

   [1]    x = 4

 By now we know this much : 

    x = 4
    y = -5x/4+1

Use the  x  value to solve for  y  

    y = -(5/4)(4)+1 = -4

Solution :

 {x,y} = {4,-4} 

500

-x+2y=17    2x+2y=-10

Answer:(-9,4)

Solve equation [1] for the variable  x  
 

  [1]    x = 2y - 17

Plug this in for variable  x  in equation [2]

   [2]    2•(2y-17) + 2y = -10
   [2]    6y = 24

 Solve equation [2] for the variable  y  

   [2]    6y = 24

   [2]    y = 4

By now we know this much : 

    x = 2y-17
    y = 4

Use the  y  value to solve for  x  

    x = 2(4)-17 = -9

Solution :

 {x,y} = {-9,4} 

Solving Systems by Substitution

100

y = -3x + 11     5x + y = 21

Answer:(5, -4)

 Solve equation [2] for the variable  y
 

  [2]    y = -5x + 21

// Plug this in for variable  y  in equation [1]

   [1]    (-5x+21) + 3x = 11
   [1]     - 2x = -10.                                      Solve equation [1] for the variable  x

   [1]    2x = 10

   [1]    x = 5

By now we know this much :

    y = -5x+21
    x = 5

 Use the  x  value to solve for  y

    y = -5(5)+21 = -4

Solution :

 {y,x} = {-4,5} 

200

x + 2y = 2     x = -4y + 2

 Answer:(2,0)

 Solve equation [2] for the variable  x

  [2]    x = 4y + 2

Plug this in for variable  x  in equation [1]

   [1]    (4y+2) + 2y = 2
   [1]    6y = 0

Solve equation [1] for the variable  y

   [1]    6y = 0

   [1]    y = 0

By now we know this much :

    x = 4y+2
    y = 0

Use the  y  value to solve for  x

    x = 4(-0/32765)+2 = 2

Solution :

 {x,y} = {2,0/32765} 

300

y = -6x + 5    -2x + y = 5

Answer:(0, 5)

 Solve equation [2] for the variable  y
 

  [2]    y = 2x + 5

 Plug this in for variable  y  in equation [1]

   [1]    (2x+5) + 6x = 5
   [1]    8x = 0

Solve equation [1] for the variable  x

   [1]    8x = 0

   [1]    x = 0

 By now we know this much :

    y = 2x+5
    x = 0

 Use the  x  value to solve for  y

    y = 2(-0/32767)+5 = 5

Solution :

 {y,x} = {5,0/32767} 

400

y = -2x + 18    x = 5

Answer:(5, 8)

Solve equation [2] for the variable  x

   [2]    x = 5

Plug this in for variable  x  in equation [1]

   [1]    y + 2•(5) = 18
   [1]    y = 8

Solve equation [1] for the variable  y

   [1]    y = 8

 By now we know this much :

    y = 8
    x = 5

We are done

Solution :

 {y,x} = {8,5} 

500

x = -3y - 8     x - 2y = -3

Answer: (-5,-1)

Solve equation [2] for the variable  x
 

  [2]    x = 2y - 3

Plug this in for variable  x  in equation [1]

   [1]    (2y-3) + 3y = -8
   [1]    5y = -5

Solve equation [1] for the variable  y

   [1]    5y = - 5

   [1]    y = - 1

By now we know this much :

    x = 2y-3
    y = -1

 Use the  y  value to solve for  x

    x = 2(-1)-3 = -5

Solution :

 {x,y} = {-5,-1} 

Simplifying Expressions

100

3x + 2x

Answer :5x

step 1Combine like terms

3x+2x

=5x

200

-r - 10r

Answer: -11r

Step 1:Combine like terms

−r−10r

−11r

300

Simplify by combining like terms:
5a + 2b - 3a + 4

Answer: 2a + 2b + 4 

Step 1:Combine like terms.                              5a+2b−3a+4

2a+2b+4

400

 2x + 1 + 7x

Answer: 9x + 1

step 1: Combine like terms

2x+1+7x

9x+1

500

-9(14p - 8) - 4p

Answer−2(65p−36)

Step 1:Distribute.                                       −9(14p−8)−4p

−126p+72−4p

Step 2:Combine like terms

−126p+72−4p

−130p+72

step 3:Common factor

−130p+72

−2(65p−36)