Question

Представьте в виде многочлена стандартного вида: 1)(x-7)*(x+1) 2)(2a-5)*(1-2a) 3)(3a-b)*(2a+b) 4)(a-b)*(2a-b-1) 5)(a+5)*(a-4) 6)(3x-1)*(3-2x) 7)(3a+b)*(b-2a) 8)(x-y)*(2x+y-3) 9)(c-7)*(c+2) 10)(5c+2)*(1-2c) 11)(3c-2d)*(d-c) 12)(a+b)*(3a-b+2)

Answer 1

1) =х в квадрате + х - 7х - 7=x в кв.-6х-7
2)=2a - 4a в квадрате - 5 + 10a = 12a - 4a в квадрате - 5
3)=6a в квадрате + 3аb - 2ab - b в квадрате = 6a в квадрате + ab - b
4)=2a в квадрате - ab - a - 2ab + b в кв.+ b = 2a в кв.+b в кв. - 3ab - a + b
5)=a в кв.- 4а + 5а - 20 =а в кв.+ а - 20
6)=9х - 6х в кв.- 3 + 2х = -6х в кв. + 11х - 3
7)=3ab - 6a в кв. + b в кв.- 2ab = -6a в кв.+ b + ab
8)=2x в кв.+ ху - 3х - 2ху - у в кв. + 3у = 2х в кв. - у в кв.-ху - 3х + 3у
9)=с в кв.+2с - 7с - 14 = с в кв.- 5с - 14
10)=5с - 10с в кв. + 2 - 4с = -10с в кв.+с +2
11)=3сd - 3с в кв. - 2d в кв. + 2cd = -3c в кв. - 2d в кв. + 5 сd
12)=3a в кв. - ab+2a+3ab-b в кв.+2b=3a в кв.- b в кв.+2ab+2a+2b

Answer 2

1) (x-7)(x+1)

To simplify this expression, we can expand it using the distributive property:

(x-7)(x+1) = x(x+1) - 7(x+1)

Expanding further:

= x^2 + x - 7x - 7

Combining like terms:

= x^2 - 6x - 7

Therefore, the expression (x-7)(x+1) simplifies to x^2 - 6x - 7.

2) (2a-5)(1-2a)

Using the distributive property, we can expand this expression:

(2a-5)(1-2a) = 2a(1-2a) - 5(1-2a)

Expanding further:

= 2a - 4a^2 - 5 + 10a

Combining like terms:

= -4a^2 + 12a - 5

So, the expression (2a-5)(1-2a) simplifies to -4a^2 + 12a - 5.

3) (3a-b)(2a+b)

Expanding this expression using the distributive property:

(3a-b)(2a+b) = 3a(2a+b) - b(2a+b)

Expanding further:

= 6a^2 + 3ab - 2ab - b^2

Combining like terms:

= 6a^2 + ab - b^2

Thus, the expression (3a-b)(2a+b) simplifies to 6a^2 + ab - b^2.

4) (a-b)(2a-b-1)

Expanding this expression using the distributive property:

(a-b)(2a-b-1) = a(2a-b-1) - b(2a-b-1)

Expanding further:

= 2a^2 - ab - a - 2ab + b^2 + b

Combining like terms:

= 2a^2 - 3ab - a + b^2 + b

Therefore, the expression (a-b)(2a-b-1) simplifies to 2a^2 - 3ab - a + b^2 + b.

5) (a+5)(a-4)

Using the distributive property, we can expand this expression:

(a+5)(a-4) = a(a-4) + 5(a-4)

Expanding further:

= a^2 - 4a + 5a - 20

Combining like terms:

= a^2 + a - 20

So, the expression (a+5)(a-4) simplifies to a^2 + a - 20.

6) (3x-1)(3-2x)

Expanding this expression using the distributive property:

(3x-1)(3-2x) = 3x(3-2x) - 1(3-2x)

Expanding further:

= 9x - 6x^2 - 3 + 2x

Combining like terms:

= -6x^2 + 11x - 3

Thus, the expression (3x-1)(3-2x) simplifies to -6x^2 + 11x - 3.

7) (3a+b)(b-2a)

Expanding this expression using the distributive property:

(3a+b)(b-2a) = (3a)(b-2a) + b(b-2a)

Expanding further:

= 3ab - 6a^2 + b^2 - 2ab

Combining like terms:

= b^2 + ab - 6a^2

Therefore, the expression (3a+b)(b-2a) simplifies to b^2 + ab - 6a^2.

8) (x-y)(2x+y-3)

Expanding this expression using the distributive property:

(x-y)(2x+y-3) = (x)(2x+y-3) - y(2x+y-3)

Expanding further:

= 2x^2 + xy - 3x - 2xy - y^2 + 3y

Combining like terms:

= 2x^2 - xy - 3x - y^2 + 3y

So, the expression (x-y)(2x+y-3) simplifies to 2x^2 - xy - 3x - y^2 + 3y.

9) (c-7)(c+2)

Using the distributive property, we can expand this expression:

(c-7)(c+2) = c(c+2) - 7(c+2)

Expanding further:

= c^2 + 2c - 7c - 14

Combining like terms:

= c^2 - 5c - 14

Thus, the expression (c-7)(c+2) simplifies to c^2 - 5c - 14.

10) (5c+2)(1-2c)

Expanding this expression using the distributive property:

(5c+2)(1-2c) = (5c)(1-2c) + 2(1-2c)

Expanding further:

= 5c - 10c^2 + 2 - 4c

Combining like terms:

= -10c^2 + c - 2

Therefore, the expression (5c+2)(1-2c) simplifies to -10c^2 + c - 2.

11) (3c-2d)(d-c)

Expanding this expression using the distributive property:

(3c-2d)(d-c) = (3c)(d-c) - 2d(d-c)

Expanding further:

= 3cd - 3c^2 - 2d^2 + 2cd

Combining like terms:

= 5cd - 3c^2 - 2d^2

Thus, the expression (3c-2d)(d-c) simplifies to 5cd - 3c^2 - 2d^2.

12) (a+b)(3a-b+2)

Expanding this expression using the distributive property:

(a+b)(3a-b+2) = a(3a-b+2) + b(3a-b+2)

Expanding further:

= 3a^2 - ab + 2a + 3ab - b^2 + 2b

Combining like terms:

= 3a^2 + 2a + 2ab - b^2 + 2b

Therefore, the expression (a+b)(3a-b+2) simplifies to 3a^2 + 2a + 2ab - b^2 + 2b.

I hope this helps! If you have any more questions, feel free to ask.