Answer this in pattern,show the solutionCube of Binomial

1.) (x+4)³
2.) (x-4)³
3.) (7m-3n)³
4.) (3xy+1)

Factoring:Factor the ff. Trinomials

1.) 6m³-9m²
2.) 6m²-12mn²+3n

Factor the difference of two square

1.) 9x²-25y²
2.)36x²-49y²
3.)32m²-98n²
4.)36p²-25

Answers

Answer 1

Answer: Cube of Binomial
1. $(x + 4)^(3)$
   $(x + 4)(x + 4)(x + 4)$
   $(x(x + 4) + 4(x + 4))(x + 4)$
   $(x(x) + x(4) + 4(x) + 4(4))(x + 4)$
   $(x^(2) + 4x + 4x + 16)(x + 4)$
   $(x^(2) + 8x + 16)(x + 4)$
   $x^(2)(x + 4) + 8x(x + 4) + 16(x + 4)$
   $x^(2)(x) + x^(2)(4) + 8x(x) + 8x(4) + 16(x) + 16(4)$
   $x^(3) + 4x^(2) + 8x^(2) + 32x + 16x + 64$
   $x^(3) + 12x^(2) + 48x+ 64$

2. $(x - 4)^(3)$
   $(x - 4)(x - 4)(x - 4)$
   $(x(x - 4) - 4(x - 4))(x - 4)$
   $(x(x) - x(4) - 4(x) + 4(4))(x - 4)$
   $(x^(2) - 4x - 4x + 16)(x - 4)$
   $(x^(2) - 8x + 16)(x - 4)$
   $x^(2)(x - 4) - 8x(x - 4) + 16(x - 4)$
   $x^(2)(x) - x^(2)(4) - 8x(x) + 8x(4) + 16(x) - 16(4)$
   $x^(3) - 4x^(2) - 8x^(2) + 32x + 16x - 64$
   $x^(3) - 12x^(2) + 48x - 64$

3. $(7m - 3n)^(3)$
   $(7m - 3n)(7m - 3n)(7m - 3n)$
   $(7m(7m - 3n) - 3n(7m - 3n))(7m - 3n)$
   $(7m(7m) - 7m(3n) - 3n(7m) + 3n(3n))(7m - 3n)$
   $(49m^(2) - 21mn - 21mn + 9n^(2))(7m - 3n)$
   $(49m^(2) - 42mn + 9n^(2))(7m - 3n)$
   $49m^(2)(7m - 3n) - 42mn(7m - 3n) + 9n^(2)(7m - 3n)$
   $49m^(2)(7m) - 49m^(2)(3n) - 42mn(7m) + 42mn(3n) + 9n^(2)(7m) - 9n^(2)(3n)$
   $343m^(3) - 147m^(2)n - 294m^(2)n + 126mn^(2) + 63mn^(2) - 27n^(3)$
   $343m^(3) - 441m^(2)n + 189mn^(2) - 27n^(3)$

4. $(3xy + 1)^(3)$
   $(3xy + 1)(3xy + 1)(3xy + 1)$
   $(3xy(3xy + 1) + 1(3xy + 1))(3xy + 1)$
   $(3xy(3xy) + 3xy(1) + 1(3xy) + 1(1))(3xy + 1)$
   $(9x^(2)y^(2) + 3xy + 3xy + 1)(3xy + 1)$
   $(9x^(2)y^(2) + 6xy + 1)(3xy + 1)$
   $9x^(2)y^(2)(3xy + 1) + 6xy(3xy + 1) + 1(3xy + 1)$
   $9x^(2)y^(2)(3xy) + 9x^(2)y^(2)(1) + 6xy(3xy) + 6xy(1) + 1(3xy) + 1(1)$
   $27x^(3)y^(3) + 9x^(2)y^(2) + 18x^(2)y^(2) + 6xy + 3xy + 1$
   $27x^(3)y^(3) + 27x^(2)y^(2) + 9xy + 1$

Factoring Trinomials
1. $6m^(3) - 9m^(2)$
   $3m^(2)(2m) + 3m^(2)(3)$
   $3m^(2)(2m + 3)$

2. $6m^(2) - 12mn^(2) + 3n$
   $3(2m^(2)) - 3(4mn^(2)) + 3(n)$
   $3(2m^(2) - 4mn^(2) + n)$

Factoring the Difference of Two Squares
1. $9x^(2) - 25y^(2)$
   $9x^(2) + 15xy - 15xy - 25y^(2)$
   $3x(3x) + 3x(5y) - 5y(3x) - 5y(5y)$
   $3x(3x + 5y) - 5y(3x + 5y)$
   $(3x - 5y)(3x + 5y)$

2. $36x^(2) - 49y^(2)$
   $36x^(2) - 42xy + 42xy - 49y^(2)$
   $6x(6x) - 6x(7y) + 7y(6x) - 7y(7x)$
   $6x(6x - 7y) + 7y(6x - 7y)$
   $(6x + 7y)(6x - 7y)$

3. $32m^(2) - 98n^(2)$
   $2(16m^(2)) - 2(49n^(2))$
   $2(16m^(2) - 49n^(2))$
   $2(16m^(2) - 28mn + 28mn - 49n^(2))$
   $2(4m(4m) - 4m(7n) + 7n(4m) - 7n(7n))$
   $2(4m(4m - 7n) + 7n(4m - 7n))$
   $2(4m + 7n)(4m - 7n)$

4. $36p^(2) - 25$
   $36p^(2) - 30p + 30p - 25$
   $6p(6p) - 6p(5) + 5(6p) - 5(5)$
   $6p(6p - 5) + 5(6p - 5)$
   $(6p + 5)(6p - 5)$

Related Questions

Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?A.f(x) = (x – 8)2 – 56 B.f(x) = (x – 4)2 + 0 C.f(x) = (x + 8)2 – 72 D.f(x) = (x + 4)2 – 32
What additional information do you need to prove that ∆LMO ≅ ∆LNO by the HL Theorem? ∠NLO ≅ ∠MLO ∠MOL ≅ ∠NOL
I don't know this operation
One number is -3 times the first number. The sum of the numbers is -4. What is the second number?
Find the missing value 2+?=-13

Question olve the following quadratic by factoring. a^(2)-4a-12=0

Answers

Answer:

a = - 2 , a = 6

Step-by-step explanation:

a² - 4a - 12 = 0

consider the factors of the constant term (- 12) which sum to give the coefficient of the a- term (- 4)

the factors are + 2 and - 6, since

+ 2 × - 6 = - 12 and + 2 - 6 = - 4

use these factors to split the a- term

a² + 2a - 6a - 12 = 0 ( factor the first/second and third/fourth terms )

a(a + 2) - 6(a + 2) = 0 ← factor out common factor (a + 2) from each term

(a + 2)(a - 6) = 0 ← in factored form

equate each factor to zero and solve for a

a + 2 = 0 ( subtract 2 from each side )

a = - 2

a - 6 = 0 ( add 6 to both sides )

a = 6

solutions are a = - 2 , a = 6

Charlie solved an equation, as shown below:Step 1: 5x = 30
Step 2: x = 30 – 5
Step 3: x = 25

Part A: Is Charlie's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)

Part B: How many solutions will this equation have? (4 points)

Answers

Part A: Charlie's answer is incorrect. Part B: There is only 1 solution for this equation.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

Charlie solved an equation;

Step 1: 5x = 30

Step 2: x = 30 – 5

Step 3: x = 25

Part A: Charlie's answer is incorrect.

In step 2 of Charlie's answer he subtracted 5 from each side. Since 5x is multiplication so, he must divide each side by 5 to get x by itself.

Step 1: 5x = 30

Step 2: x = 30/5

Step 3: x = 6

Part B: There is only 1 solution for this equation.

Learn more about linear equations;

brainly.com/question/10413253

#SPJ2

Part A: Charlie's answer is incorrect
In step 2 of Charlie's answer he subtracted 5 from each side. Since 5x is multiplication, he must DIVIDE each side by 5 to get x by itself. The problem should have worked out like this...

Step 1: 5x = 30
Step 2: x = 30/5
Step 3: x = 6

Part B: There is only 1 solution for this problem.

Functions f(x) and g(x) are shown below.f(x) = x^2
g(x) = x^2 8x 16
In which direction and by how many units should f(x) be shifted to obtain g(x)?

Answers

We can factor g(x) as $(x+4)^2$ . Clearly, g(x) is simply f(x+4), so f(x) should increase each x by 4 to achieve the same result as g(x). Therefore, f(x) should be shifted 4 units in the positive-x (or right) direction.

100 students take a course pass/fail. If they pass they get 4 points towards their GPA, if they fail they get 0. If 90 students pass, what is the mean and standard deviation (to 1 decimal) of the points earned?Mean: ________a0

Standard Deviation:________ a1

Answers

Formulas
Mean = total sum of points / # of data
[Stantard deviation] ^ 2 = {Sum of [every data - mean]^2 } / [number of data - 1]

Procedure:

Mean = total sum of points / # of data

Total sum of points = point of pass + point of fail

points of pass = 90*4 = 360
point of fail = 10*0 = 0
Total sum of points = 360

Number of data = 100

Mean = 360/100 = 3.6

[Stantard deviation] ^ 2 = {Sum of [every data - mean]^2 } / [number of data - 1]

[Sum of every data - mean]^2 = 90*[4 -3.6]^2 + 10* [0 - 3.6]^2 = 14.4 + 129.6 = 144

[Stantard deviation] ^ 2 = [144]/[100-1] =144/99

Standar deviation = √(144/99) = 1.206

If: 2=6, 3=12, 4=20, 5=30, 6=42, 9=??

Answers

2*3=6, 3*4=12, 4*5=20, 5*6=30, 6*7=42, 7*8=56, 8*9=72, 9*10=90. 90 is your final answer

your answer would be 9=72 they are just multiplying the first number by 3 then 4 then 5 and so on and so on

Wil offer 15 points to whoever can PLEASE answer this for me!! ill help with your question too

Answers

The area of the circle is 16*16*pi=256pi. We can calculate 3/4 of the circle's area for the part not represented by the triangle and the shaded area, and then add in the triangle. 3/4 of the circle's area is 192pi.

The triangle is a right triangle with two legs of length 16. Therefore, it's area is 16*16/2=128, and the total area is 192pi+128, or 731.2.

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Factor the expression.15n−18 Enter your answers in the boxes to complete the factored expression.

Answer this in pattern,show the solutionCube of Binomial1.) (x+4)³2.) (x-4)³3.) (7m-3n)³4.) (3xy+1)Factoring:Factor the ff. Trinomials1.) 6m³-9m²2.) 6m²-12mn²+3nFactor the difference of two square1.) 9x²-25y²2.)36x²-49y²3.)32m²-98n²4.)36p²-25

Answers

Related Questions

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What is a linear equation?

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Answer this in pattern,show the solutionCube of Binomial

1.) (x+4)³
2.) (x-4)³
3.) (7m-3n)³
4.) (3xy+1)

Factoring:Factor the ff. Trinomials

1.) 6m³-9m²
2.) 6m²-12mn²+3n

Factor the difference of two square

1.) 9x²-25y²
2.)36x²-49y²
3.)32m²-98n²
4.)36p²-25