Question

Розкладіть на множники вирази: 1) х(а + b) - a - b;2) x(m + n) - 7m - 7n;3) ax - 2a + 3x - 6;4) 2mx - 3m - 4x + 6;5) 12a2b2 - 6abc + 3ac2 - 6a2bc - c + 2ab;6) xyz + x2y2 + 3x4y5 + 3x3y4z - xy - z.Розв'яжіть рівняння:1) 12x2 - 6x = 0;2) 10x2 + x = 0;3) y(5 - y) = 0.​

Answer 1

Ответ:

Объяснение:

1) x(a+b)-a-b=x(a+b)-(a+b)=(x-1)(a+b)

2) x(m+n)-7m-7n=x(m+n)-7(m+n)=(x-7)(m+n)

3) ax-2a+3x-6=a(x-2)+3(x-2)=(a+3)(x-2)

4) 2mx-3m-4x+6=m(2x-3)-2(2x-3)=(m-2)(2x-3)

5) 12a2b2-6abc+3ac2-6a2bc-c+2ab= 6ab(2ab-c)-3ac(2ab-c)+(2ab-c)=(6ab-3ac+1)(2ab-c)

6) xyz+x2y2+3x4y5+3x3y4z-xy-z=xy(z+xy)+3x3y4(xy+z)-(xy+z)=(xy+3x3y4-1)(xy+z)

1) 12*2-6x=0

24-6x=o

-6x=-24

x=4

2) 10*2+x=0

20+x=0

x=-20

3) y(5-y)=0

y=0 або 5-y=0

y=5

Answer 2

Розкладіть на множники вирази:

1) х(а + b) - a - b

To factorize this expression, let's look for common factors: х(а + b) - a - b = ха + хb - a - b

Now, let's group the terms: (ха - a) + (хb - b)

Now, we can factor out the common factor from each group: а(х - 1) + b(х - 1)

Finally, we can factor out the common factor (х - 1): (а + b)(х - 1)

So, the expression х(а + b) - a - b can be factored as (а + b)(х - 1).

2) x(m + n) - 7m - 7n

To factorize this expression, let's look for common factors: x(m + n) - 7m - 7n

Now, let's group the terms: (xm - 7m) + (xn - 7n)

Now, we can factor out the common factor from each group: m(x - 7) + n(x - 7)

Finally, we can factor out the common factor (x - 7): (m + n)(x - 7)

So, the expression x(m + n) - 7m - 7n can be factored as (m + n)(x - 7).

3) ax - 2a + 3x - 6

To factorize this expression, let's look for common factors: ax - 2a + 3x - 6

Now, let's group the terms: (ax + 3x) + (-2a - 6)

Now, we can factor out the common factor from each group: x(a + 3) - 2(a + 3)

Finally, we can factor out the common factor (a + 3): (x - 2)(a + 3)

So, the expression ax - 2a + 3x - 6 can be factored as (x - 2)(a + 3).

4) 2mx - 3m - 4x + 6

To factorize this expression, let's look for common factors: 2mx - 3m - 4x + 6

Now, let's group the terms: (2mx - 4x) + (-3m + 6)

Now, we can factor out the common factor from each group: 2x(m - 2) - 3(m - 2)

Finally, we can factor out the common factor (m - 2): (2x - 3)(m - 2)

So, the expression 2mx - 3m - 4x + 6 can be factored as (2x - 3)(m - 2).

5) 12a^2b^2 - 6abc + 3ac^2 - 6a^2bc - c + 2ab

To factorize this expression, let's look for common factors: 12a^2b^2 - 6abc + 3ac^2 - 6a^2bc - c + 2ab

Now, let's group the terms: (12a^2b^2 - 6abc + 2ab) + (3ac^2 - 6a^2bc - c)

Now, we can factor out the common factor from each group: 6ab(2ab - c + 1) + c(3a^2 - 6ab - 1)

So, the expression 12a^2b^2 - 6abc + 3ac^2 - 6a^2bc - c + 2ab can be factored as 6ab(2ab - c + 1) + c(3a^2 - 6ab - 1).

6) xyz + x^2y^2 + 3x^4y^5 + 3x^3y^4z - xy - z

To factorize this expression, let's look for common factors: xyz + x^2y^2 + 3x^4y^5 + 3x^3y^4z - xy - z

There are no common factors that can be factored out from all the terms in this expression. So, the expression cannot be further factorized.

Розв'яжіть рівняння:

1) 12x^2 - 6x = 0

To solve this equation, let's factor out the common factor: 6x(2x - 1) = 0

Now, set each factor equal to zero and solve for x: 6x = 0 or 2x - 1 = 0

For the first equation, divide both sides by 6: x = 0

For the second equation, add 1 to both sides and divide by 2: 2x = 1 x = 1/2

So, the solutions to the equation 12x^2 - 6x = 0 are x = 0 and x = 1/2.

2) 10x^2 + x = 0

To solve this equation, let's factor out the common factor: x(10x + 1) = 0

Now, set each factor equal to zero and solve for x: x = 0 or 10x + 1 = 0

For the first equation, x = 0.

For the second equation, subtract 1 from both sides and divide by 10: 10x = -1 x = -1/10

So, the solutions to the equation 10x^2 + x = 0 are x = 0 and x = -1/10.

3) y(5 + y) = 0

To solve this equation, let's set each factor equal to zero and solve for y: y = 0 or 5 + y = 0

For the first equation, y = 0.

For the second equation, subtract 5 from both sides: y = -5

So, the solutions to the equation y(5 + y) = 0 are y = 0 and y = -5.