Doctor, I’ve swallowed the
film out of my camera!
The factorised form of the expressions and
the letter beside each of them gives the puzzle code.
D = 6x – 3 =
E = 8 – 2x =
G = 15x + 10 =
H = –2x + 1 =
I = 12x + 20 =
L = 2xy – 3y =
N = 18 – 42x =
O = –2x – 2 =
P = 2xy – 8y =
S = –12x – 21 =
T = xy – 2x =
V = 56x – 35 =
E = 6xy + 3x =
L = 8xy – 72y =
N = –x + 2 =
E = 6x – 14 =
O = –xy + y =
P = 3x – 12 =
E = –8x – 24 =
S = 3xy – 2y =
T = 6xy – 10y =
O = –49 – 28x =
H = –20x – 25 =
6(3 – 7x) –y(x – 1) x(y – 2) –5(4x + 5) 4(3x + 5) –(x – 2)
3(2x – 1) –8(x + 3) 7(8x – 5) 3x(2y + 1) y(2x – 3) –2(x + 1) 3(x – 4) y(3x – 2)
2(4 – x)
–7(7 + 4x)
8y(x – 9)
–(2x – 1) 2y(x – 4)
2y(3x – 5)
2(3x – 7)
–3(4x + 7)
5(3x + 2
To find the factorized form of the given expressions, we need to factor out common terms.
D = 6x – 3 = 3(2x – 1)
E = 8 – 2x = -2(x – 4)
G = 15x + 10 = 5(3x + 2)
H = –2x + 1 = -1(2x – 1)
I = 12x + 20 = 4(3x + 5)
L = 2xy – 3y = y(2x – 3)
N = 18 – 42x = -6(7x – 3)
O = –2x – 2 = -2(x + 1)
P = 2xy – 8y = 2y(x – 4)
S = –12x – 21 = -3(4x + 7)
T = xy – 2x = x(y – 2)
V = 56x – 35 = 7(8x – 5)
what would the code be ?
The code is a sequence of letters obtained by taking the letter beside each factorized expression in the given list.
In this case, the code would be:
CODE: D E G H I L N O P S T V
i mean for the activity
To find the code for the activity, we need to take the first letter of each factorized expression in the given list.
In this case, the code for the activity would be:
CODE: DEGHILONOPSTV
To find the puzzle code, we need to factorize each of the given expressions and take note of the letter next to it.
Let's start with the expressions:
D = 6x – 3 = 3(2x - 1)
E = 8 – 2x = -2(x - 4)
G = 15x + 10 = 5(3x + 2)
H = –2x + 1 = -1(2x - 1)
I = 12x + 20 = 4(3x + 5)
L = 2xy – 3y = y(2x - 3)
N = 18 – 42x = -6(7x - 3)
O = –2x – 2 = -2(x + 1)
P = 2xy – 8y = 2y(x - 4)
S = –12x – 21 = -3(4x + 7)
T = xy – 2x = x(y - 2)
V = 56x – 35 = 7(8x - 5)
E = 6xy + 3x = 3x(2y + 1)
L = 8xy – 72y = 8y(x - 9)
N = –x + 2 = -1(x - 2)
E = 6x – 14 = 2(3x - 7)
O = –xy + y = y(1 - x)
P = 3x – 12 = 3(x - 4)
E = –8x – 24 = -8(x + 3)
S = 3xy – 2y = y(3x - 2)
T = 6xy – 10y = 2y(3x - 5)
O = –49 – 28x = -7(7 + 4x)
H = –20x – 25 = -5(4x + 5)
6(3 – 7x) – y(x – 1) = 3(2 - 7x) - (x - 1)
x(y – 2) – 5(4x + 5) = x(y - 2) - 5(4x + 5)
4(3x + 5) – (x – 2) = 4(3x + 5) - (x - 2)
3(2x – 1) – 8(x + 3) = 3(2x - 1) - 8(x + 3)
7(8x – 5) = 7(8x - 5)
3x(2y + 1) – y(2x – 3) = 3x(2y + 1) - y(2x - 3)
2(x + 1) – 3(x – 4) = 2(x + 1) - 3(x - 4)
y(3x – 2) = y(3x - 2)
2(4 – x) = 2(4 - x)
–7(7 + 4x) = -7(7 + 4x)
8y(x – 9) = 8y(x - 9)
–(2x – 1) = -(2x - 1)
2y(x – 4) = 2y(x - 4)
2y(3x – 5) = 2y(3x - 5)
2(3x – 7) = 2(3x - 7)
–3(4x + 7) = -3(4x + 7)
5(3x + 2) = 5(3x + 2)
Now, we can look at the factorized forms of the expressions and their corresponding letters:
D = 3(2x - 1) = 3D
E = -2(x - 4) = -2E
G = 5(3x + 2) = 5G
H = -1(2x - 1) = -1H
I = 4(3x + 5) = 4I
L = y(2x - 3) = L
N = -6(7x - 3) = -6N
O = -2(x + 1) = -2O
P = 2y(x - 4) = 2P
S = -3(4x + 7) = -3S
T = x(y - 2) = T
V = 7(8x - 5) = 7V
E = 3x(2y + 1) = 3E
L = 8y(x - 9) = 8L
N = -1(x - 2) = -1N
E = 2(3x - 7) = 2E
O = y(1 - x) = O
P = 3(x - 4) = 3P
E = -8(x + 3) = -8E
S = y(3x - 2) = S
T = 2y(3x - 5) = 2T
O = -7(7 + 4x) = -7O
H = -5(4x + 5) = -5H
Now, let's combine the letters in the order they appear to get the puzzle code:
DEGHI
LNEO
PESOT
OV
ELNEOPESH
To find the factorized form of the expressions, we need to factorize each expression by identifying common factors and applying the distributive property if necessary. Let's go through each expression step by step:
D = 6x – 3
To factorize this expression, we can see that both terms have a common factor of 3. Factoring out 3 gives us:
D = 3(2x - 1)
E = 8 – 2x
In this expression, there are no common factors between the terms. So, we can't factorize it any further.
G = 15x + 10
Similar to expression E, there are no common factors between the terms, so it can't be factorized.
H = –2x + 1
Similarly, there are no common factors in the expression H, so it can't be factorized.
I = 12x + 20
Here, both terms have a common factor of 4. Factoring out 4 gives us:
I = 4(3x + 5)
L = 2xy – 3y
In this expression, both terms have a common factor of y. Factoring out y gives us:
L = y(2x - 3)
N = 18 – 42x
Here, both terms have a common factor of 6. Factoring out 6 gives us:
N = 6(3 - 7x)
O = –2x – 2
In this expression, both terms have a common factor of 2. Factoring out 2 gives us:
O = 2(-x - 1)
However, usually when simplifying or factorizing, we don't leave a negative sign in front of the parentheses. We can rewrite it as:
O = -2(x + 1)
P = 2xy – 8y
In this expression, both terms have a common factor of 2y. Factoring out 2y gives us:
P = 2y(x - 4)
S = –12x – 21
Similar to expression O, both terms have a common factor of 3. Factoring out 3 gives us:
S = 3(-4x - 7)
T = xy – 2x
In this expression, both terms have a common factor of x. Factoring out x gives us:
T = x(y - 2)
V = 56x – 35
Here, both terms have a common factor of 7. Factoring out 7 gives us:
V = 7(8x - 5)
Now, we have gone through all the expressions and factorized them where possible. The next step is to find the puzzle code by taking the letter beside each expression. Let's combine all the letters:
D, E, G, H, I, L, N, O, P, S, T, V, E, L, N, E, O, P, E, S, T, O, H
The puzzle code is: DEGHI-LNOPSTOPESTO
Note: I assumed that the repeated expressions (E, L, N, O, and H) were meant to be the same expressions and did not factorize them twice.