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3 years ago

Choose the correct simplification of the expression (2x − 6)(3x2 − 3x − 6).

Mathematics

2 answers:

Lady bird [3.3K]3 years ago

6 0

Answer:

Option A is correct.

Correct simplification of the given expression = $6x^3-24x^2+6x+36$

Step-by-step explanation:

Given the expression: $(2x-6)(3x^2-3x-6)$

The following steps required for the multiplication of polynomials are:

Distribute each terms of the first polynomial to every term of the second polynomial.

Combine like terms

Apply these steps to the given expressions;

$2x(3x^2-3x-6) -6(3x^2-3x-6)$

when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.

⇒ $6x^3-6x^2-12x -18x^2 +18x +36$

Combine like terms;

$6x^3-24x^2+6x+36$

Therefore, the correct simplification of the given expression is, $6x^3-24x^2+6x+36$

seraphim [82]3 years ago

3 0

If you would like to solve (2x - 6) * (3x^2 - 3x - 6), you can do this using the following steps:

(2x - 6) * (3x^2 - 3x - 6<span>) = 2x * 3x^2 - 2x * 3x - 2x * 6 - 6 * 3x^2 + 6 * 3x + 6 * 6 = 6x^3 - 6x^2 - 12x - 18x^2 + 18x + 36 = 6x^3 - 24x^2 + 6x + 36
</span>
The correct result would be <span>6x^3 - 24x^2 + 6x + 36.</span>

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2 years ago

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Is (2,1) a solution of 3y<2x+5

Nikitich [7]

Answer:

Step-by-step explanation:

Plug in the x and y values and you should get 3<9

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3 years ago

A teachers desk is 5.5 meters long a students desk is 220 centimeters long what is the difference in the length in centimeters b

Mama L [17]

so if 5.5 is in meter let change it to cm because the question want us to give the answer in cm.

$1cm = 0.01meter$

$to \: turn \: meters \: into \: \\ cm \: we \: have \: to \: multiply \: by \: 100$

now we multiply 5.5 times 100 which is equal to 550.

next we subtract 550 - 220= 330.

finally, the difference between a teacher and student is 330cm .meaning the teacher's desk is 330 cm longer or taller than the student.

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3 years ago

Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Vilka [71]

Answer: Choice B) 1/3, 1/4, 1/5, 1/6

=============================================

Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

a_1 = ( 2! )/( 3! )

a_1 = ( 2*1 )/( 3*2*1 )

a_1 = 2/6

a_1 = 1/3

The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

------------

Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

a_2 = 6/24

a_2 = 1/4

The second term is 1/4

------------

Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

a_3 = 1/5

The third term is 1/5

------------

Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

------------

The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

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3 years ago