Question

• 1. Выполните действия: а) (2а2 - За + 1) - (7а2 - 5а); б) 3х (4х2 - х). • 2. Вынесите общий множитель за скобки: а) 2ху - 3ху2; б) 8b4 + 2b3. • 3. Решите уравнение 7 - 4 (3х - 1) = 5 (1 - 2х). • 4. В трех шестых классах 91 ученик. В 6 «А» на 2 ученика меньше, чем в 6 «Б», а в 6 «В» на 3 ученика больше, чем в 6 «Б». Сколько учащихся в каждом классе? 5. Решите уравнение . 6. Упростите выражение 3х (х + у + с) - 3у (х - у - с) - 3с (х + у - с).

Answer 1

• 1. Выполните действия:

а) (2а² - За + 1) - (7а² - 5а)=2a²-3a+1-7a²+5a= -5a²+2a+1;

б) 3х (4х² - х)=12x³-3x².  

• 2. Вынесите общий множитель за скобки:

а) 2ху - 3ху²=xy(2-3y);

б) 8b⁴ + 2b³=2b³(4b+1).  

• 3. Решите уравнение

7 - 4 (3х - 1) = 5 (1 - 2х)

7-12x+4=5-10x

7+4-5=12x-10x

6=2x

x=3  

• 4. В трех шестых классах 91 ученик. В 6 «А» на 2 ученика меньше, чем в 6 «Б», а в 6 «В» на 3 ученика больше, чем в 6 «Б». Сколько учащихся в каждом классе?

пусть в 6А = х учеников; в 6Б= х+2 ученика; в 6В=х+2+3=х+5 учеников

х+х+2+х+5=91

3х+7=91

3х=84

х=28

В 6А=28; в 6Б=30; в 6В=33

5. Решите уравнение .  

условия нет

6. Упростите выражение

3х (х + у + с) - 3у (х - у - с) - 3с (х + у - с)=

=3x²+3xy+3xc-3xy+3y²+3yc-3xc-3yc+3c²=

=3x²+3y²+3c²=3(x²+y²+c²)

Answer 2

1. Выполните действия:

а) (2а^2 - За + 1) - (7а^2 - 5а)

To perform this operation, we need to simplify and combine like terms. Let's start by distributing the negative sign to the terms inside the second parenthesis:

(2а^2 - За + 1) - 7а^2 + 5а

Next, let's combine like terms:

2а^2 - 7а^2 - За + 5а + 1

Simplifying further:

-5а^2 - За + 6а + 1

The simplified expression is -5а^2 - За + 6а + 1.

б) 3х(4х^2 - х)

To simplify this expression, we need to distribute the 3х to each term inside the parenthesis:

3х * 4х^2 - 3х * х

Simplifying further:

12х^3 - 3х^2

The simplified expression is 12х^3 - 3х^2.

2. Вынесите общий множитель за скобки:

а) 2ху - 3ху^2

In this expression, the common factor is ху. Let's factor it out:

ху(2 - 3у)

The factored expression is ху(2 - 3у).

б) 8b^4 + 2b^3

In this expression, the common factor is b^3. Let's factor it out:

b^3(8b + 2)

The factored expression is b^3(8b + 2).

3. Решите уравнение 7 - 4(3х - 1) = 5(1 - 2х).

To solve this equation, we'll start by simplifying both sides:

7 - 4(3х - 1) = 5(1 - 2х)

Let's distribute the -4 and 5 to their respective terms:

7 - 12х + 4 = 5 - 10х

Simplifying further:

11 - 12х = 5 - 10х

Next, let's isolate the variable terms on one side and the constant terms on the other side:

-12х + 10х = 5 - 11

Combine like terms:

-2х = -6

Finally, divide both sides by -2 to solve for х:

х = -6 / -2

Simplifying further:

х = 3

The solution to the equation is х = 3.

4. В трех шестых классах 91 ученик. В 6 «А» на 2 ученика меньше, чем в 6 «Б», а в 6 «В» на 3 ученика больше, чем в 6 «Б». Сколько учащихся в каждом классе?

To solve this problem, let's assign variables to represent the number of students in each class. Let's say the number of students in 6 "A" is A, the number of students in 6 "B" is B, and the number of students in 6 "V" is V.

We are given the following information:

A + B + V = 91 (Total number of students in all three classes)

A = B - 2 (Number of students in 6 "A" is 2 less than in 6 "B")

V = B + 3 (Number of students in 6 "V" is 3 more than in 6 "B")

We can use these equations to solve for the number of students in each class.

Let's start by substituting the values of A and V in terms of B into the equation A + B + V = 91:

(B - 2) + B + (B + 3) = 91

Simplifying further:

3B + 1 = 91

Next, let's isolate the variable term on one side:

3B = 91 - 1

3B = 90

Finally, divide both sides by 3 to solve for B:

B = 90 / 3

B = 30

Now that we know the number of students in 6 "B," we can substitute this value back into the equations for A and V:

A = 30 - 2 A = 28

V = 30 + 3 V = 33

Therefore, there are 28 students in 6 "A," 30 students in 6 "B," and 33 students in 6 "V."

5. Решите уравнение .

I apologize, but the equation you provided seems to be missing. Could you please provide the equation so that I can help you solve it?

6. Упростите выражение 3х(х + у + с) - 3у(х - у - с) - 3с(х + у - с).

To simplify this expression, let's distribute each term to the terms inside the parentheses:

3х * х + 3х * у + 3х * с - 3у * х + 3у * у + 3у * с - 3с * х - 3с * у + 3с * с

Simplifying further:

3х^2 + 3ху + 3хс - 3ух + 3у^2 + 3ус - 3сх - 3су + 3с^2

Next, let's combine like terms:

(3х^2 - 3ух - 3сх) + (3ху + 3у^2 - 3су) + (3хс + 3ус + 3с^2)

We can factor out a common factor of 3 from each group of terms:

3(х^2 - ух - сх) + 3(ху + у^2 - су) + 3(хс + ус + с^2)

The simplified expression is 3(х^2 - ух - сх) + 3(ху + у^2 - су) + 3(хс + ус + с^2).