Question

a) (x + 2)(x – 5) -3x(1 - 2x), б) (а + 3)(а - 2) + (a - 3)(a + 6), в) (x - 7)(3x - 2) – (5x + 1)(2x – 4).​

Answer 1

Объяснение:

а)

(х+2)(х-5)-3х(1-2х)=х²-5х+2х-10-3х+6х²=

=7х²-6х-10

б)

(а+3)(а-2)+(а-3)(а+6)=

=а²-2а+3а-6+а²+6а-3а-18=

=2а²+4а-24

в)

(х-7)(3х-2)-(5х+1)(2х-4)=

=3х²-2х-21х+14-(10х²-20х+2х-4)=

=3х²-2х-21х+14-10х²+20х-2х+4=

= -7х²-5х+18

Answer 2

Let's simplify each of these expressions step by step:

a) (x + 2)(x - 5) - 3x(1 - 2x)

First, let's expand each of the products:

(x + 2)(x - 5) = x^2 - 5x + 2x - 10 = x^2 - 3x - 10

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

Now, we can subtract the second expression from the first:

x^2 - 3x - 10 - (3x - 6x^2)

Now, distribute the negative sign to both terms inside the parentheses:

x^2 - 3x - 10 - 3x + 6x^2

Combine like terms:

x^2 + 6x^2 - 3x - 3x - 10

7x^2 - 6x - 10

So, the simplified expression is 7x^2 - 6x - 10.

b) (a + 3)(a - 2) + (a - 3)(a + 6)

First, let's expand each of the products:

(a + 3)(a - 2) = a^2 - 2a + 3a - 6 = a^2 + a - 6

(a - 3)(a + 6) = a^2 + 6a - 3a - 18 = a^2 + 3a - 18

Now, we can add the two expressions together:

(a^2 + a - 6) + (a^2 + 3a - 18)

Now, combine like terms:

a^2 + a + a^2 + 3a - 6 - 18

2a^2 + 4a - 24

Now, factor out a 2:

2(a^2 + 2a - 12)

Now, let's factor the expression inside the parentheses:

a^2 + 2a - 12 can be factored as (a + 4)(a - 3).

So, the simplified expression is 2(a + 4)(a - 3).

c) (x - 7)(3x - 2) - (5x + 1)(2x - 4)

First, let's expand each of the products:

(x - 7)(3x - 2) = 3x^2 - 2x - 21x + 14 = 3x^2 - 23x + 14

(5x + 1)(2x - 4) = 10x^2 - 20x + 5x - 4 = 10x^2 - 15x - 4

Now, we can subtract the second expression from the first:

(3x^2 - 23x + 14) - (10x^2 - 15x - 4)

Now, distribute the negative sign to both terms inside the parentheses:

3x^2 - 23x + 14 - 10x^2 + 15x + 4

Combine like terms:

(3x^2 - 10x^2) + (-23x + 15x) + (14 + 4)

-7x^2 - 8x + 18

So, the simplified expression is -7x^2 - 8x + 18.