Question

Помогите пожалуйстаа! очень срочно! умоляю 1.Упростить: a) (а-4)^2-a(2a-8) б) х^6*х^4/x^2 2.Разложить на множители: а) 36-х^2; б) 27-b^3; в) b^3+1; г) х^2-18х+81; д) 36b^2+12b+1; е) 7ху^2-14x^2; ж) 25х-х^3; з) 5а-аb+5с-сb. 3.Решить уравнение: х (х-4)=(х+3)^2. 4.Построить график функции у=3-3х. Принадлежит ли графику этой функции точка А (9;-24) ? 5.На 1-м участке было в 5 раз больше кустов смородины, чем на 2-м. После того, как на 2-й участок пересадили с 1-го участка 50 кустов и ещё посадили на 2-м участке 60 кустов, то на обоих участках кустов стало поровну. Сколько кустов смородины было на каждом участке первоначально?

Answer 1

1/

a) (а-4)^2-a(2a-8)=a^2-8a+16-2a^2+8a=16- a^2

б) х^6*х^4/x^2= х^6+4/x^2= х^8

2/

a)36-х^2=(6-x)(6+x)

б) 27-b^3=(9-b)(36+6b+b^2)

в) b^3+1=(b+1)(b^2-b+1)

г) х^2-18х+81=(x-9)^2

д) 36b^2+12b+1=(6b+1)^2

е) 7ху^2-14x^2=7x(y^2-2x)

ж) 25х-х^3= х(5^2-x^2)=x(5-x)(5+x)

з) 5а-аb+5с-сb=-b(a+c)+5(a+c)= (a+c)(b-5)

Answer 2

1. Упростить:

a) $(a-4)^2-a(2a-8)$

To simplify this expression, we can expand the square and then distribute the terms: $(a-4)^2 = a^2 - 8a + 16$

Now, let's distribute the $-a$ to the terms inside the parentheses: $a(2a-8) = 2a^2 - 8a$

Finally, we can combine like terms: $(a-4)^2 - a(2a-8) = a^2 - 8a + 16 - (2a^2 - 8a)$

Simplifying further: $a^2 - 8a + 16 - 2a^2 + 8a = -a^2 + 16$

So, the simplified expression is $-a^2 + 16$.

2. Разложить на множители:

a) $36-x^2$

To factorize this expression, we can use the difference of squares formula: $36-x^2 = (6+x)(6-x)$

So, the factored form of $36-x^2$ is $(6+x)(6-x)$.

б) $27-b^3$

To factorize this expression, we can use the difference of cubes formula: $27-b^3 = (3-b)(9+3b+b^2)$

So, the factored form of $27-b^3$ is $(3-b)(9+3b+b^2)$.

в) $b^3+1$

This expression cannot be factored further since it does not have any common factors or any special formulas to apply.

г) $x^2-18x+81$

To factorize this expression, we can use the perfect square trinomial formula: $x^2-18x+81 = (x-9)^2$

So, the factored form of $x^2-18x+81$ is $(x-9)^2$.

д) $36b^2+12b+1$

This expression cannot be factored further since it does not have any common factors or any special formulas to apply.

е) $7xu^2-14x^2$

To factorize this expression, we can factor out the common factor of $7x$: $7xu^2-14x^2 = 7x(u^2-2x)$

So, the factored form of $7xu^2-14x^2$ is $7x(u^2-2x)$.

ж) $25x-x^3$

To factorize this expression, we can factor out the common factor of $x$: $25x-x^3 = x(25-x^2)$

So, the factored form of $25x-x^3$ is $x(25-x^2)$.

з) $5a-ab+5c-cb$

To factorize this expression, we can factor out the common factor of $a$ and $c$: $5a-ab+5c-cb = a(5-b) + c(5-b)$

Now, we can factor out the common factor of $(5-b)$: $a(5-b) + c(5-b) = (5-b)(a+c)$

So, the factored form of $5a-ab+5c-cb$ is $(5-b)(a+c)$.

3. Решить уравнение:

$x+(x-4)=(x+3)^2$

To solve this equation, we can start by expanding the square on the right side: $x+(x-4)=x^2+6x+9$

Now, let's simplify the equation: $2x-4=x^2+6x+9$

Rearranging the terms to bring all terms to one side: $x^2+4x+13=0$

This is a quadratic equation. To solve it, we can use the quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

For our equation, $a=1$, $b=4$, and $c=13$. Plugging in these values: $x=\frac{-4\pm\sqrt{4^2-4(1)(13)}}{2(1)}$

Simplifying further: $x=\frac{-4\pm\sqrt{16-52}}{2}$

Since the discriminant ($b^2-4ac$) is negative, the equation has no real solutions. Therefore, the equation $x+(x-4)=(x+3)^2$ has no solution.

4. Построить график функции у=3-3х. Принадлежит ли графику этой функции точка А (9;-24)?

To plot the graph of the function $y=3-3x$, we can start by creating a table of values by substituting different values of $x$ and calculating the corresponding values of $y$.

| x | y | |---|---| | -2 | 9 | | -1 | 6 | | 0 | 3 | | 1 | 0 | | 2 | -3 | | 3 | -6 |

Plotting these points on a graph, we can see that the graph of the function is a straight line with a slope of -3 and a y-intercept of 3.

Now, let's check if point A (9, -24) belongs to the graph of this function. Substituting the x-coordinate of point A into the equation, we get: $y=3-3(9)=-24$

Since the calculated y-value (-24) matches the y-coordinate of point A, we can conclude that point A (9, -24) does belong to the graph of the function.

Therefore, the graph of the function $y=3-3x$ does pass through the point A (9, -24).

5. На 1-м участке было в 5 раз больше кустов смородины, чем на 2-м. После того, как на 2-й участок пересадили с 1-го участка 50 кустов и ещё посадили на 2-м участке 60 кустов, то на обоих участках кустов стало поровну. Сколько кустов смородины было на каждом участке первоначально?

Let's assume that the number of currant bushes on the second plot is represented by the variable $x$. According to the given information, the number of currant bushes on the first plot is 5 times greater than the number on the second plot, so we can represent it as $5x$.

After transferring 50 bushes from the first plot to the second plot and planting an additional 60 bushes on the second plot, the number of bushes becomes equal on both plots.

So, we can set up the following equation: $5x - 50 = x + 60$

Simplifying the equation: $4x = 110$

Dividing both sides by 4: $x = 27.5$

Since the number of bushes cannot be a fraction, we can conclude that there was an error in the given information or the problem statement.

Therefore, it is not possible to determine the initial number of currant bushes on each plot based on the given information.