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4 years ago

Simplify the expression 3a(3-a)+3(a^2-3)+3a

Mathematics

2 answers:

Readme [11.4K]4 years ago

4 0

Answer:

3 (4 a - 3)

Step-by-step explanation:

Simplify the following:

3 a (3 - a) + 3 (a^2 - 3) + 3 a

3 a (3 - a) = 9 a - 3 a^2:

9 a - 3 a^2 + 3 (a^2 - 3) + 3 a

3 (a^2 - 3) = 3 a^2 - 9:

3 a^2 - 9 - 3 a^2 + 9 a + 3 a

Grouping like terms, 3 a^2 - 3 a^2 + 9 a + 3 a - 9 = (9 a + 3 a) - 9 + (-3 a^2 + 3 a^2):

(9 a + 3 a) - 9 + (-3 a^2 + 3 a^2)

9 a + 3 a = 12 a:

12 a - 9 + (-3 a^2 + 3 a^2)

3 a^2 - 3 a^2 = 0:

12 a - 9

Factor 3 out of 12 a - 9:

Answer: 3 (4 a - 3)

Gre4nikov [31]4 years ago

3 0

Answer:

12a−9

Step-by-step explanation:

Distribute:

=(3a)(3)+(3a)(−a)+(3)(a2)+(3)(−3)+3a

=9a+−3a2+3a2+−9+3a

Combine Like Terms:

=9a+−3a2+3a2+−9+3a

=(−3a2+3a2)+(9a+3a)+(−9)

=12a+−9

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IN A CLASS OF 60 STUDENTS, 25 PLAYS BASKETBALL, 2O PLAY VOLLEYBALL, AND 10 STUDENTS PLAY BOTH OF THEM. HOW MANY STUDENTS PLAY NE

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Answer:

Step-by-step explanation:

We'll compare it with the study of sets, the most noticeable operation of which is:

<u>n(A ∪ B) = n(A) + n(B) - n(A ∩ B)</u>

where,

n(A ∪ B) is the Union Set, i. e, the set that contains all the elements

n(A) is a subset of the Union Set

n(B) is another subset of the Union Set, and

n(A ∩ B) is the Intersection Set ,i.e, the set contains common elements from both A and B sets.

<h3><u>In the question:</u></h3>

n(A ∪ B) = ? (<em>the total number of students in the class who are into the above mentioned sports)</em>

Let set A contains the students who play basketball and set B, the students who play Volleyball.

n(A) = 25
n(B) = 20

10 students play both of them, i. e.,

n(A ∩ B) = 10 (<em>as 10 students have common sports - Volleyball and Basketball</em>)

<u>Using the above operation:</u>

=> n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

=> n(A ∪ B) = 25 + 20 - 10

=> n(A ∪ B) = 35

<h3><u>Final Step to the Answer:</u></h3>

<u>The total number of students in the class </u>

= students into the given sports + students who don't play any of them

Total number of students in the class is 60
Total number fo students playing basketball and volleyball is 35

The students who play neither = 60 - 35

= 25

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